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By providing mathematical estimates, this paper answers a fundamental question—"what leads to Stokes drift"? Although overwhelmingly understood for water waves, Stokes drift is a generic mechanism that stems from kinematics and occurs in any nontransverse wave in fluids. To showcase its generality, we undertake a comparative study of the pathline equation of sound (1D) and intermediate-depth water (2D) waves. Although we obtain a closed-form solution x(t) for the specific case of linear sound waves, a more generic and meaningful approach involves the application of asymptotic methods and expressing variables in terms of the Lagrangian phase θ. We show that the latter reduces the 2D pathline equation of water waves to 1D. Using asymptotic methods, we solve the respective pathline equation for sound and water waves, and for each case, we obtain a parametric representation of particle position x(θ) and elapsed time t(θ). Such a parametric description has allowed us to obtain second-order accurate expressions for the time duration, horizontal displacement, and average horizontal velocity of a particle in the crest and trough phases. All these quantities are of higher magnitude in the crest phase in comparison to the trough phase, leading to a forward drift, i.e., Stokes drift. We also explore particle trajectory due to second-order Stokes waves and compare it with linear waves. While finite amplitude waves modify the estimates obtained from linear waves, the understanding acquired from linear waves is generally found to be valid. [ABSTRACT FROM AUTHOR]

The vertical buoyancy flux Bf under the turbulent thermal wind (TTW) balance B f TTW plays an important role in restratifying the surface mixed layer in winter. So far, most of the global ocean models are too coarse to resolve this process. In this paper, a scale-aware parameterization is proposed for B f TTW and implemented in a hierarchy of regional ocean simulations over the winter Kuroshio Extension with horizontal resolutions ranging from 27 to 1 km. The parameterization depends on the Coriolis parameter, model-simulated turbulent vertical viscosity, horizontal density gradient, and a scaling relationship to adjust for the effects of model horizontal resolution on the simulated horizontal density gradient. It shows good skills in reconciling the difference between B f TTW in the coarse-resolution simulations (27, 9, and 3 km) and in the 1-km simulation where B f TTW is well resolved. Furthermore, implementation of the parameterization improves the simulated stratification in the surface mixed layer in coarse-resolution simulations. [ABSTRACT FROM AUTHOR]

Large-amplitude internal solitary waves were recently observed in a coastal plain estuary and were hypothesized to evolve from an internal lee wave generated at the channel–shoal interface. To test this mechanism, a 3D nonhydrostatic model with nested domains and adaptive grids was used to investigate the generation of the internal solitary waves and their subsequent nonlinear evolution. A complex sequence of wave propagation and transformation was documented and interpreted using the nonlinear wave theory based on the Korteweg–de Vries equation. During the ebb tide a mode-2 internal lee wave is generated by the interaction between lateral flows and channel–shoal topography. This mode-2 lee wave subsequently propagates onto the shallow shoal and transforms into a mode-1 wave of elevation as strong mixing on the flood tide erases stratification in the bottom boundary layer and the lower branch of the mode-2 wave. The mode-1 wave of elevation evolves into an internal solitary wave due to nonlinear steepening and spatial changes in the wave phase speed. As the solitary wave of elevation continues to propagate over the shoaling bottom, the leading edge moves ahead as a rarefaction wave while the trailing edge steepens and disintegrates into a train of rank-ordered internal solitary waves, due to the combined effects of shoaling and dispersion. Strong turbulence in the bottom boundary layer dissipates wave energy and causes the eventual destruction of the solitary waves. In the meantime, the internal solitary waves can generate elevated shear and dissipation rate in local regions. Significance Statement: In the coastal ocean nonlinear internal solitary waves are widely recognized to play an important role in generating turbulent mixing, modulating short-term variability of nearshore ecosystem, and transporting sediment and biochemical materials. However, their effects on shallow and stratified estuaries are poorly known and have been rarely studied. The nonhydrostatic model simulations presented in this paper shed new light into the generation, propagation, and transformation of the internal solitary waves in a coastal plain estuary. [ABSTRACT FROM AUTHOR]

Surface waves grow through a mechanism in which atmospheric pressure is offset in phase from the wavy surface. A pattern of low atmospheric pressure over upward wave orbital motions (leeward side) and high pressure over downward wave orbital motions (windward side) travels with the water wave, leading to a pumping of kinetic energy from the atmospheric boundary layer into the waves. This pressure pattern persists above the air–water interface, modifying the turbulent kinetic energy in the atmospheric wave-affected boundary layer. Here, we present field measurements of wave-coherent atmospheric pressure and velocity to elucidate the transfer of energy from the atmospheric turbulence budget into waves through wave-coherent atmospheric pressure work. Measurements show that the phase between wave-coherent pressure and velocity is shifted slightly above 90° when wind speed exceeds the wave phase speed, allowing for a downward energy flux via pressure work. Although previous studies have reported wave-coherent pressure, to the authors' knowledge, these are the first reported field measurements of wave-coherent pressure work. Measured pressure work cospectra are consistent with an existing model for atmospheric pressure work. The implications for these measurements and their importance to the turbulent kinetic energy budget are discussed. Significance Statement: Surface waves grow through a pattern of atmospheric pressure that travels with the water wave, acting as a pump against the water surface. The pressure pumping, sometimes called pressure work, or the piston pressure, results in a transfer of kinetic energy from the air to the water that makes waves grow larger. To conserve energy, it is thought that the pressure work on the surface must extract energy from the mean wind profile or wind turbulence that sets the shape of the wind speed with height. In this paper, we present direct measurements of pressure work in the atmosphere above surface waves. We show that the energy extracted by atmospheric pressure work fits existing models for how waves grow and a simple model for how waves reduce energy in the turbulent kinetic energy budget. To our knowledge, these are the first reported field measurements of wave-coherent pressure work. [ABSTRACT FROM AUTHOR]

Deep ocean passages are advantageous sites for long-term monitoring of deep transport and other physical properties relevant to climate. Rotating hydraulic theory provides potential for simplifying monitoring strategy by reducing the number of quantities that need to be measured. However, the applicability of these theories has been limited by idealizations such as restriction to zero or uniform potential vorticity (pv) and to channels with rectangular cross sections. Here the relationship between the flow characteristics in a canonical sea strait and its upstream condition is studied using uniform pv rotating hydraulic theory and a reduced-gravity shallow-water numerical model that allows for variation in pv. The paper is focused mainly on the sensitivity of the hydraulic solution to the strait geometry. We study the dynamics of channels with continuously varying (parabolic) cross sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. The results show that far enough from the channel entrance, the hydraulically controlled flow in the strait is insensitive to the basin circulation regardless of parabolic curvature. The controlled transport relation is derived for the case of uniform pv theory. Comparing the model to theory, we find that the measurement of the wetted edges of the interface height at the critical section can be used to estimate the volume flux. Based on this finding, we suggest three monitoring strategies for transport estimation and compare the estimates with the observed values at the Faroe Bank Channel. The results showed that the estimated transports are within the range of observed values. Significance Statement: The paper investigates the relationship between the flow characteristics in an idealized sea strait and its upstream condition using rotating hydraulic theory and numerical modeling. We study the dynamics of channels with continuously varying (parabolic) cross sections to account for the rounded nature of sea-strait topographies and potentially improve monitoring strategies for realistic channel geometries. We suggest three monitoring strategies for transport estimation and apply the methods to the Faroe Bank Channel. Our estimates of dense water transport are within the range of observed values. This is significant, because the suggested monitoring strategies only require 1–3 measurements to estimate the transport at a given passage and can be used to guide observing systems. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the problem of wind–wave interaction with emphasis on strong winds. For these events, it is assumed that nonlinearity is so large that the slope of the wind waves has reached a limiting steepness. Recent observations suggest that the drag decreases with wind in the strong wind speed regime. In this paper, we try to explain this. In the first step, we introduce a model for surface gravity waves and calculate explicitly the background roughness length from the original approach of Janssen. It is found that for young, steep wind sea, the background roughness length almost vanishes, giving a reduced drag. In addition, it is shown that for steep waves, the slowing down of the wind by waves is a nonlinear process; hence, the growth rate of the waves by wind depends in a nonlinear fashion on the wave spectrum. For strong winds, it is found that, as waves are typically steep, this nonlinear effect gives a further reduction of the wind input. As a consequence, in these extreme circumstances, the drag coefficient decreases with wind. [ABSTRACT FROM AUTHOR]

Energy exchanges between large-scale ocean currents and mesoscale eddies play an important role in setting the large-scale ocean circulation but are not fully captured in models. To better understand and quantify the ocean energy cycle, we apply along-isopycnal spatial filtering to output from an isopycnal 1/32° primitive equation model with idealized Atlantic and Southern Ocean geometry and topography. We diagnose the energy cycle in two frameworks: 1) a non-thickness-weighted framework, resulting in a Lorenz-like energy cycle, and 2) a thickness-weighted framework, resulting in the Bleck energy cycle. This paper shows that framework 2 is more useful for studying energy pathways when an isopycnal average is used. Next, we investigate the Bleck cycle as a function of filter scale. Baroclinic conversion generates mesoscale eddy kinetic energy over a wide range of scales and peaks near the deformation scale at high latitudes but below the deformation scale at low latitudes. Away from topography, an inverse cascade transfers kinetic energy from the mesoscales to larger scales. The upscale energy transfer peaks near the energy-containing scale at high latitudes but below the deformation scale at low latitudes. Regions downstream of topography are characterized by a downscale kinetic energy transfer, in which mesoscale eddies are generated through barotropic instability. The scale- and flow-dependent energy pathways diagnosed in this paper provide a basis for evaluating and developing scale- and flow-aware mesoscale eddy parameterizations. Significance Statement: Blowing winds provide a major energy source for the large-scale ocean circulation. A substantial fraction of this energy is converted to smaller-scale eddies, which swirl through the ocean as sea cyclones. Ocean turbulence causes these eddies to transfer part of their energy back to the large-scale ocean currents. This ocean energy cycle is not fully simulated in numerical models, but it plays an important role in transporting heat, carbon, and nutrients throughout the world's oceans. The purpose of this study is to quantify the ocean energy cycle by using fine-scale idealized numerical simulations of the Atlantic and Southern Oceans. Our results provide a basis for how to include unrepresented energy exchanges in coarse global climate models. [ABSTRACT FROM AUTHOR]

In this paper we present the analytical derivation of a local water mass transformation (WMT) framework for an individual water column. We exactly formulate the mapping of the governing equations from geopotential coordinates to an arbitrary tracer space. Unique definitions for the local effective vertical diasurface fluxes are given. In tracer space we derive new relations between the local diatracer fluxes and the mixing per tracer class. The key relation between the effective vertical diatracer velocity and the mixing per tracer class directly formulates how the overturning circulation is linked to local tracer variance dissipation. Horizontal integration of the governing equations in tracer space and the relations between the diatracer quantities finally recovers the well-known integral WMT formulations. [ABSTRACT FROM AUTHOR]

Fronts and near-inertial waves (NIWs) are energetic motions in the upper ocean that have been shown to interact and provide a route for kinetic energy (KE) dissipation of balanced oceanic flows. In this paper, we study these KE exchanges using an idealized model consisting of a two-dimensional geostrophically balanced front undergoing strain-induced semigeostrophic frontogenesis and internal wave (IW) vertical modes. The front–IW KE exchanges are quantified separately during two frontogenetic stages: an exponential sharpening stage that is characterized by a low Rossby number and is driven by the imposed strain (i.e., mesoscale frontogenesis), followed by a superexponential sharpening stage that is characterized by an O (1) Rossby number and is driven by the convergence of the secondary circulation (i.e., submesoscale frontogenesis). It is demonstrated that high-frequency IWs quickly escape the frontal zone and are very efficient at extracting KE from the imposed geostrophic strain field through the deformation shear production (DSP). Part of the extracted KE is then converted to wave potential energy. On the contrary, NIWs remain locked to the frontal zone and readily exchange energy with the ageostrophic frontal circulation. During the exponential stage, NIWs extract KE from the geostrophic strain through DSP and transfer it to the frontal secondary circulation via the ageostrophic shear production (AGSP) mechanism. During the superexponential stage, a newly identified mechanism, convergence production (CP), plays an important role in the NIW KE budget. The CP transfers KE from the convergent ageostrophic secondary circulation to the NIWs and largely cancels out the KE loss due to the AGSP. This CP may explain previous findings of KE transfer enhancement from balanced motions to IWs in frontal regions of realistic ocean models. We provide analytical estimates for the aforementioned energy exchange mechanisms that match well the numerical results. This highlights that the strength of the exchanges strongly depends on the frontal Rossby and Richardson numbers. Significance Statement: Fronts with large horizontal density and velocity gradients are ubiquitous in the upper ocean. They are generated by a process known as frontogenesis, which is often initialized by straining motions of mesoscale balanced circulations. Here we examine the energy exchanges between fronts and internal waves in an idealized configuration, aiming to elucidate the mechanisms that can drain energy from oceanic balanced circulations. We identify a new mechanism for energy transfers from the frontal circulation to near-inertial internal waves called convergence production. This mechanism is especially effective during the later stages of frontogenesis when the convergent ageostrophic secondary circulation that develops is strong. [ABSTRACT FROM AUTHOR]

Multidecadal variability on time scales between 20 and 70 years have been observed in the time series of North Atlantic SST.Many mechanisms have been proposed to explain multidecadal variabilities in the Atlantic. Generally, it is the interaction between the meridional overturning circulation (MOC) and North Atlantic surface buoyancy distribution that sustains this variability, with buoyancy anomalies either due to ocean-only processes or to air--sea interactions. In this context, the role of the Arctic Ocean, especially its freshwater flux into the North Atlantic, has been underappreciated. Bering Strait, the only oceanic pathway between the Pacific Ocean and the Arctic Ocean, has been found important in Arctic Ocean freshwater budget and in modulating the time-averaged state and long-term response of the MOC to highlatitude buoyancy forcing anomalies, via freshwater transport between the Pacific and Atlantic Oceans. In this paper, we use idealized configurations that include a Pacific-like wide basin and an Atlantic-like narrow basin. The two basins are connected both in the south and north to longitudinally periodic channels, representing the Southern Ocean and the Arctic Ocean, respectively. The Pacific-like basin is opened to the north only through a shallow and narrow strait, while the Atlantic-like basin is fully open to the north. With the goal of studying the role of Bering Strait in the multidecadal variability, we find that the freshwater transport from the Bering Strait forms a tongue structure along the western boundary of the narrow basin, which enhances the local horizontal density gradient. The western boundary region becomes unstable to large-scale baroclinic anomalies, giving rise to multidecadal variability. [ABSTRACT FROM AUTHOR]

Previous satellite estimates of internal tides are usually based on 25 years of sea surface height (SSH) data from 1993 to 2017 measured by exact-repeat (ER) altimetry missions. In this study, new satellite estimates of internal tides are based on 8 years of SSH data from 2011 to 2018 measured mainly by nonrepeat (NR) altimetry missions. The two datasets are labeled ER25yr and NR8yr, respectively. NR8yr has advantages over ER25yr in observing internal tides because of its shorter time coverage and denser ground tracks. Mode-1 M2 internal tides are mapped from both datasets following the same procedure that consists of two rounds of plane wave analysis with a spatial bandpass filter in between. The denser ground tracks of NR8yr make it possible to examine the impact of window size in the first-round plane wave analysis. Internal tides mapped using six different windows ranging from 40 to 160 km have almost the same results on global average, but smaller windows can better resolve isolated generation sources. The impact of time coverage is studied by comparing NR8yr160km and ER25yr160km, which are mapped using 160-km windows in the first-round plane wave analysis. They are evaluated using independent satellite altimetry data in 2020. NR8yr160km has larger model variance and can cause larger variance reduction, suggesting that NR8yr160km is a better model than ER25yr160km. Their global energies are 43.6 and 33.6 PJ, respectively, with a difference of 10 PJ. Their energy difference is a function of location. Significance Statement: Our understanding of internal tides is mainly limited by the scarcity of field measurements with sufficient spatiotemporal resolution. Satellite altimetry offers a unique technique for observing and predicting internal tides on a global scale. Previous satellite observations of internal tides are mainly based on 25 years of data from exact-repeat altimetry missions. This paper demonstrates that internal tides can be mapped using 8 years of data made by nonrepeat altimetry missions. The new dataset has shorter time coverage and denser ground tracks; therefore, one can examine the impact of window size and time coverage on mapping internal tides from satellite altimetry. A comparison of models mapped from the two datasets sheds new light on the spatiotemporal variability of internal tides. [ABSTRACT FROM AUTHOR]

Many wind wave spectrum models provide excellent wave height prediction given the input of wind speed and wave age. Their quantification of the surface roughness, on the other hand, varies considerably. The ocean surface roughness is generally represented by the mean square slope, and its direct measurement in open ocean remains a challenging task. Microwave remote sensing from space delivers ocean surface roughness information. Satellite platforms offer global coverage in a broad range of environmental conditions. This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling. The analysis presented in this paper shows that over two orders of magnitude of the wavenumber range (0.3–30 rad m−1), the spectral components follow a power function relating the dimensionless spectrum and the ratio between wind friction velocity and wave phase speed. The power function exponent is about 0.38, which is considerably smaller than unity as expected from the classical equilibrium spectrum function. It may suggest that wave breaking is not only an energy sink but also a source of roughness generation covering a wideband of wavelengths about 20 m and shorter. Significance Statement: This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling that is critical to the investigation of air–sea interaction and ocean remote sensing. The analysis presented in this paper suggests that wave breaking is not only an energy sink but also a generation source of surface roughness covering a wide band of wavelengths about 20 m and shorter. [ABSTRACT FROM AUTHOR]

There have been several numerical models developed to represent the phase-averaged flow in the surf zone, which is characterized by kD less than unity, where k is wavenumber and D is the water column depth. The classic scenario is that of surface gravity waves progressing onto a shore that create an offshore undertow current. In fact, in some models, flow velocities are parameterized assuming the existence of an undertow. The present approach uses the full vertically dependent continuity and momentum equations and the vertically dependent wave radiation stress in addition to turbulence equations. The model is applied to data that feature measurements of wave properties and also cross-shore velocities. In this paper, both the data and the model application are unidirectional and the surface stress is nil, representing the simplest surf zone application. Breaking waves are described empirically. Special to the surf zone, it is found that a simple empirical adjustment of the radiation stress enables a favorable comparison with data. Otherwise, the model applies to the open ocean with no further empiricism. A new bottom friction algorithm had been derived and is introduced in this paper. In the context of the turbulence transport model, the algorithm is relatively simple. [ABSTRACT FROM AUTHOR]

The wind drag on the sea surface is characterized by the aerodynamic roughness of the sea surface, z0, which is regulated by surface wind waves. Many studies have related the dimensionless form of z0 to the wave age parameter estimated from spectral peak information. These parametric relationships have been well developed for the wind-driven sea but not for mixed seas. Based on an analysis using observations from a fixed platform in the northern South China Sea, the deficiency of the spectral peak information in the parametric description z0 when swells dominate is indicated. Instead, a consistent parametric description of z0 can be obtained by using the wave age estimated from the mean wave period, and normalizing z0 by the mean wavelength. Normalizing z0 by the significant wave height introduces a spurious residual dependence of z0 on the wave steepness. A parametric relationship is developed between the dimensionless z0 (normalized by the mean wavelength) and the wave age from the mean wave period. A comparison of this new relationship to the wind-speed-only formulation in COARE 3.5 is provided. Significance Statement: In this paper, a consistent parametric description of the wave age dependence of the surface aerodynamic roughness is presented, with a wide range of sea states from dominant wind-driven seas to mixed seas in which the swells are dominant. [ABSTRACT FROM AUTHOR]

The potential role of the New England seamount chain (NESC) on the Gulf Stream pathway and variability has been long recognized, and the series of numerical experiments presented in this paper further emphasize the importance of properly resolving the NESC when modeling the Gulf Stream. The NESC has a strong impact on the Gulf Stream pathway and variability, as demonstrated by comparison experiments with and without the NESC. With the NESC removed from the model bathymetry, the Gulf Stream remains a stable coherent jet much farther east than in the experiment with the NESC. The NESC is the leading factor destabilizing the Gulf Stream and, when it is not properly resolved by the model's grid, its impact on the Gulf Stream's pathway and variability is surprisingly large. A high-resolution bathymetry, which better resolves the New England seamounts (i.e., narrower and rising higher in the water column), leads to a tighter Gulf Stream mean path that better agrees with the observed path and a sea surface height variability distribution that is in excellent agreement with the observations. [ABSTRACT FROM AUTHOR]

The Indo-Pacific Ocean appears exponentially stratified between 1- and 3-km depth with a decay scale on the order of 1 km. In his celebrated paper "Abyssal recipes," W. Munk proposed a theoretical explanation of these observations by suggesting a pointwise buoyancy balance between the upwelling of cold water and the downward diffusion of heat. Assuming a constant upwelling velocity w and turbulent diffusivity κ, the model yields an exponential stratification whose decay scale is consistent with observations if κ ∼ 10−4 m2 s−1. Over time, much effort has been made to reconcile Munk's ideas with evidence of vertical variability in κ, but comparably little emphasis has been placed on the even stronger evidence that w decays toward the surface. In particular, the basin-averaged w nearly vanishes at 1-km depth in the Indo-Pacific. In light of this evidence, we consider a variable-coefficient, basin-averaged analog of Munk's budget, which we verify against a hierarchy of numerical models ranging from an idealized basin-and-channel configuration to a coarse global ocean simulation. Study of the budget reveals that the decay of basin-averaged w requires a concurrent decay in basin-averaged κ to produce an exponential-like stratification. As such, the frequently cited value of 10−4 m2 s−1 is representative only of the bottom of the middepths, whereas κ must be much smaller above. The decay of mixing in the vertical is as important to the stratification as its magnitude. Significance Statement: Using a combination of theory and numerical simulations, it is argued that the observed magnitude and shape of the global ocean stratification and overturning circulation appear to demand that turbulent mixing increases quasi-exponentially toward the ocean bottom. Climate models must therefore prescribe such a vertical profile of turbulent mixing in order to properly represent the heat and carbon uptake accomplished by the global overturning circulation on centennial and longer time scales. [ABSTRACT FROM AUTHOR]

The Agulhas Current (AC) is a critical component of global ocean circulation. However, due to a lack of multidecadal observations, it is not clear how the AC has changed in response to anthropogenic forcing. A recent observational study suggests a broadening and slight weakening of the AC in the past few decades, while others suggest a strengthening of the AC during the historical period. In this paper, we find substantial internal variability of the AC on decadal to multidecadal time scales in high-resolution models. We show that the AC consistently exhibits two modes of decadal and multidecadal (i.e., low frequency) variability in a series of high-resolution climate models: a uniform mode that is largely associated with changes in the AC strength and a dipole mode that is mainly related to width changes of the AC. We demonstrate that the uniform mode is mainly forced externally by the decadal variations of the wind field and presents a decline under global warming, suggesting a weakening of the AC in response to anthropogenic forcing. The dipole mode, on the other hand, is mainly due to internal dynamics and does not show a trend during the historical period. Using a quasigeostrophic model that captures the dipole mode, we attribute the dipole mode to low-frequency potential vorticity changes in the western boundary, driven by a divergence of relative potential vorticity due to eddy activity. Thus, our results present further context for the interpretation of the AC responses in a changing climate based on a short observational record. [ABSTRACT FROM AUTHOR]

The authors thank Nof et al. for their comments on the authors' paper 'On the steadiness of separating meandering currents.' The authors' paper was motivated by a series of papers by Nof et al. Under a certain set of conditions (reduced gravity, steady state, no meridional velocity at outflow, and parallel outflow), Nof et al. showed that a separating and retroflecting frictionless current cannot be steady because of a momentum imbalance. The main conclusion of the authors' paper was that they agree with the Nof et al. result that a momentum imbalance exists and extended the proof to all possible configurations of retroflecting currents, even including friction. The authors' results point to a new mechanism for the generation of variability in the ocean that is not related to dynamical instability of the flow. The main claim in the comments is that the authors incorrectly argued in the appendix that the steady-state solutions presented by Nof et al. in several papers fulfill the extra constraint u2 = g′ h. In the original paper, the authors showed that it follows from the geostrophic assumption stated implicitly in all these Nof et al. papers, because the flow is assumed to be parallel. Nof et al. now argue that the flow is only approximately geostrophic in all Nof et al. papers. The authors show in this reply that for steady weakly meandering outflows approximate geostrophy does lead to a momentum imbalance paradox as Nof et al. claim. However, for a steady strongly meandering outflow, approximate geostrophy is not enough and one has to use the method explored by van Leeuwen and De Ruijter to derive a momentum imbalance paradox. [ABSTRACT FROM AUTHOR]

This paper presents analyses of drifters with drogues at different depths—1, 10, 30, and 50 m—that were deployed in the Mediterranean Sea to investigate frontal subduction and upwelling. Drifter trajectories were used to estimate divergence, vorticity, vertical velocity, and finite-size Lyapunov exponents (FTLEs) and to investigate the balance of terms in the vorticity equation. The divergence and vorticity are O(f) and change sign along trajectories. Vertical velocity is O(1 mm s−1), increases with depth, indicates predominant upwelling with isolated downwelling events, and sometimes changes sign between 1 and 50 m. Vortex stretching is one of the significant terms, but not the only one, in the vorticity balance. Two-dimensional FTLEs are 2 × 10−5 s−1 after 1 day, 2 times as large as in a 400-m-resolution numerical model. Three-dimensional FTLEs are 50% larger than 2D FTLEs and are dominated by the vertical shear of horizontal velocity. Bootstrapping suggests uncertainty levels of ~10% of the time-mean absolute values for divergence and vorticity. Analysis of simulated drifters in a model suggests that drifter-based estimates of divergence and vorticity are close to the Eulerian model estimates, except when drifters get aligned into long filaments. Drifter-based vertical velocity is close to the Eulerian model estimates at 1 m but differs at deeper depths. The errors in the vertical velocity are largely due to the lateral separation between drifters at different depths and are partially due to only measuring at four depths. Overall, this paper demonstrates how drifters, heretofore restricted to 2D near-surface observations, can be used to learn about 3D flow properties throughout the upper layer of the water column. Significance Statement: Drifting buoys, or drifters, are one of the oldest instruments in physical oceanography and have been used to study near-surface horizontal currents throughout the World Ocean. However, in flows with large vertical velocity or vertical shear, currents and transport properties change with depth, so conventional near-surface drifters are of limited use. This paper shows that a simultaneous release of drifters with drogues at different depths allows observing and quantifying both horizontal and vertical structure of the flow. Specifically, we present analyses of drifters with drogues at 1, 10, 30, and 50 m, which were deployed in the Mediterranean Sea in 2018. Drifter data are used to quantify such important flow properties as divergence, vorticity, vertical velocity, and finite-time Lyapunov exponents and to investigate the vorticity equation balance throughout the top 50 m of the water column. [ABSTRACT FROM AUTHOR]

Around Hopen Island, the satellite images and experiments with drifting buoys describe the movement of the drifting ice and depict tidally generated trapped motion. An analytical solution is applied to investigate the trapping phenomenon. A general solution is achieved by the superposition of the incident and reflected (scattered) waves for an elliptically shaped island above the critical latitude. The incident wave simulates the tidal wave propagation toward the island and its prominent feature, an amphidromic point located to the southeast from Hopen Island. The analytical solution for the reflected wave is constructed in elliptic coordinates. Tide amplitudes and cophase lines are analyzed in the island's vicinity and compared to observations and numerical model results. A simulated drift of Lagrangian water particles constructed with the help of analytical solutions reproduces well the observed clockwise trapped motion of the drifting buoy near Hopen Island. Since the resonance may amplify the semidiurnal incident tide, we have also investigated the natural modes of water oscillations near the island. While this paper focuses on the details of the model used at the specific site of Hopen Island, a similar trapping analysis can be applied to circular or elliptic islands that have a small scale relative to the barotropic Rossby deformation radius. Significance Statement: This study aims to understand how the semidiurnal tide propagates and generates strong currents near Hopen Island in the Barents Sea. The trapping of the semidiurnal (M2) tide around Hopen Island leads to an organized dipole structure in sea level, which rotates clockwise. The dipole generates maximum amplitudes of water surface elevation and the strong current near the south and north tips of the island. The abrupt sea level change induced by the dipole sets up often violent currents, which, together with drifting ice, can be dangerous for navigation. The strong tidal currents generate permanent clockwise circulation around the islands, which is essential for biological life and waste disposal as material disposed of near the islands will be trapped for an extended time. Our investigation elucidates the role of dipoles in the local enhancement of tides around the islands. [ABSTRACT FROM AUTHOR]

Moored observations and a realistic, tidally forced 3D model are presented of flow and internal-tide-driven turbulence over a supercritical 3D fan in southeastern Luzon Strait. Two stacked moored profilers, an acoustic Doppler current profiler, and a thermistor string measured horizontal velocity, density, and salinity over nearly the entire water column every 1.5 h for 50 days. Observed dissipation rate computed from Thorpe scales decays away from the bottom and shows a strong spring–neap cycle; observed depth-integrated dissipation rate scales as U BT 2.5 ± 0.6 where UBT is the barotropic velocity. Vertical velocities are strong enough to be comparable at times to the vertical profiling speed of the moored profilers, requiring careful treatment to quantify bias in dissipation rate estimates. Observations and the model are in reasonable agreement for velocity, internal wave displacement and depth-integrated dissipation rate, allowing the model to be used to understand the 3D flow. Turbulence is maximum following the transition from up-fan to down-fan flow, consistent with breaking lee waves advected past the mooring as seen previously at the Hawaiian Ridge, but asymmetric flow arises because of the 3D topography. Observed turbulence varies by a factor of 2 over the four observed spring tides as low-frequency near-bottom flow changes, but the exact means for inclusion of such low-frequency effects is not clear. Our results suggest that for the extremely energetic turbulence associated with breaking lee waves, dissipation rates may be quantitatively predicted to within a factor of 2 or so using numerical models and simple scalings. Significance Statement: This paper describes deep ocean turbulence caused by strong tidal and low-frequency meandering flows over and around a three-dimensional bump, using moored observations and a computer simulation. Such information is important for accurately including these effects in climate simulations. The observations and model agree well enough to be able to use both to synthesize a coherent picture. The observed and modeled turbulence scale as the cube of the tidal speed as expected from theory, but low-frequency flows complicate the picture. We also demonstrate the underestimation of the turbulence that can result when vertical profiling rates are comparable to the internal wave velocities. [ABSTRACT FROM AUTHOR]

The Southern Hemisphere temperature has experienced obvious changes with great spatial differences over the past several decades. Most regions show extreme warming, especially those located at 35°–55°S. In contrast, subsurface cooling exists between 15° and 35°S in the Indian and Pacific basins. The subsurface temperature and salinity change can be divided into spiciness change and heave components. The results show the warming due to isopycnal movement being largely offset by significant spiciness cooling at middepth. Surface warming and subduction into the interior ocean account for subsurface spiciness cooling near 45°S, while surface freshening and penetration along isopycnals are more important to the subsurface spiciness cooling farther north. The isobaric temperature change is associated with pure warming and pure heaving, and the subsurface cooling observed in the Indian and Pacific subtropics is predominantly attributed to pure heaving. This study provides a quantitative estimate of the relative contribution of surface temperature, salinity change, and circulation adjustment in subsurface temperature change, highlighting the importance of circulation change in producing subsurface cooling. Further research is needed to understand why different processes dominate in different ocean sections. Significance Statement: While the global ocean is warming, the subsurface temperature change exhibits a significant regional disparity. This paper attempts to explain the deep-reaching warming at 35°–55°S and cooling at 15°–35°S based on three historical observation datasets. We find that the cooling mostly occurs between 400 and 1000 m in the south Indian and Pacific subtropics (15°–35°S), which is attributed to pure heaving, indicating the importance of circulation change in these regions. The midlatitude warming (35°–55°S) is mainly caused by the pure warming process, which is related to heat uptake at the subpolar surface and northward and downward heat transport. The spiciness cooling near 45°S is mainly driven by the subduction of the surface warming signal while the freshening process has a stronger impact on spiciness cooling farther north. [ABSTRACT FROM AUTHOR]

The Kuroshio intrusion into the South China Sea (SCS) in summer is weak and has rarely been reported by in situ observations. Here, we describe a new form of Kuroshio water intrusion that is strongest during the summer, the North Luzon Warm Eddy (NLWE), which is an anticyclonic eddy originating north of Luzon Island. From early July to mid-September 2018, two NLWEs moving northwestward were captured by a mooring array consisting of 27 current- and pressure-recording inverted echo sounders (CPIESs). The three-dimensional CPIES estimates reveal that the NLWEs carried large amounts of saline Kuroshio waters (S > 34.7 psu) in the subsurface, which was also evidenced by Argo float profiles. The Kuroshio intrusion was confined to waters shallower than the 14.8°C isotherm. Historical data for NLWEs suggest that they occur mostly during the summer but are absent between November and March, which is attributed to seasonal wind stress curl (WSC). However, because the seasonal signal of WSC during summer is small, intraseasonal WSC is directly responsible for the generation of NLWEs. Significance Statement: This paper describes a new type of Kuroshio water intrusion into the South China Sea (SCS)—the North Luzon Warm Eddy (NLWE), which is an anticyclonic eddy generated north of Luzon Island. The eddy mostly occurs during summer when the Kuroshio intrusion is commonly considered the weakest. From observations of a large CPIES array, we provide a cradle-to-grave picture of the NLWE. NLWEs are estimated to contribute almost half of the westward Luzon Strait transport during the summer and, as such, play an important role in the seasonal stratification and circulation in the northeastern SCS. [ABSTRACT FROM AUTHOR]

The K-profile parameterization (KPP) is a common method to model turbulent fluxes in regional and global oceanic models. Many versions of KPP exist in the oceanic sciences community, and one of their main differences is how they take the effects of nonbreaking waves into account. Although there is qualitative consensus that nonbreaking waves enhance vertical mixing due to the ensuing Langmuir circulations, there is no consensus on the quantitative aspects and modeling approach. In this paper we use a recently developed method to estimate both components of KPP (the diffusive term, usually called local, and the nondiffusive component, usually called nonlocal) based on numerically simulated turbulent fluxes without any a priori assumptions about their scaling or their shape. Through this method we show that the cubic shape usually used in KPP is not optimal for wavy situations and propose new ones. Furthermore, we show that the formulation for the nondiffusive fluxes, which currently only depend on the presence of surface buoyancy fluxes, should also take wave effects into account. We also investigate how the application of these changes to KPP improves the representation of turbulent fluxes in a diagnostic approach when compared with previous models. [ABSTRACT FROM AUTHOR]

In this paper, the overturning responses to wind stress changes of an eddying ocean and a non-eddying ocean are compared. Differences are found in the deep overturning cell in the low-latitude North Atlantic Ocean with substantial implications for the deep western boundary current (DWBC). In an ocean-only twin experiment with one eddying and one non-eddying configuration of the MPI ocean model, two different forcings are being applied: the standard NCEP forcing and the NCEP forcing with 2× surface wind stress. The response to the wind stress doubling in the Atlantic meridional overturning circulation is similar in the eddying and the non-eddying configuration, showing an increase by about 4 Sv (~25%; 1 Sv ≡ 106 m3 s−1). In contrast, the DWBC responds with a speedup in the non-eddying configuration and a slowdown in the eddying configuration. This paper demonstrates that the DWBC slowdown in the eddying configuration is largely balanced by eddy vorticity fluxes. Because those fluxes are not resolved and also not captured by an eddy parameterization in the non-eddying configuration, such a DWBC slowdown is likely not to occur in non-eddying ocean models, which therefore might not capture the whole range of overturning responses. Furthermore, evidence is provided that the balancing effect of the eddies is not a passive reaction to a remotely triggered DWBC slowdown. Instead, deep eddies that are sourced from the upper ocean provide an excess input of relative vorticity that then actively forces the DWBC mean flow to slow down. [ABSTRACT FROM AUTHOR]

The internal wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial representation of the IW cascade. In this work, vertical spectral KE flux is decomposed into catalyst, source, and destination vertical modes and frequency bands of nonlinear scattering, a framework that allows for the discernment of different types of nonlinear interactions involving both waves and eddies. Energy transfer within the supertidal IW continuum is found to be strongly dependent on resolution. Specifically, at a horizontal grid spacing of 1/48°, most KE in the supertidal continuum arrives there from lower-frequency modes through a single nonlinear interaction, whereas at 1/384° and with sufficient vertical resolution KE transfers within the supertidal IW continuum are comparable in size to KE transfer from lower-frequency modes. Additionally, comparisons are made with existing theoretical and observational work on energy pathways in the IW continuum. Induced diffusion (ID) is found to be associated with a weak forward frequency transfer within the supertidal IW continuum. ID is also limited to the highest vertical wavenumbers and is more sensitive to resolution relative to spectrally local interactions. At the same time, ID-like processes involving high-vertical-wavenumber near-inertial and tidal waves as well as low-vertical-wavenumber eddy fields are substantial, suggesting that the processes giving rise to a Garrett–Munk-like spectra in the present numerical simulation and perhaps the real ocean may be more varied than in idealized or wave-only frameworks. [ABSTRACT FROM AUTHOR]

The winter–summer transition in the southern South China Sea (SCS) western boundary current (WBC) is studied. Two categories have been identified. In case 1, the southern SCS WBC transition in the lower layer (below the thermocline) lags that in the upper layer (above the thermocline). In case 2, there is no transition lag at full depth. In both categories, the geostrophic balance dominates the transition. In case 1, the upper layer geostrophic balance is dominated by the sea surface height pressure gradient (SSHPG) and Coriolis forcing during southern SCS WBC transition. Therefore, there is no transition lag with depth in the upper layer. Below the thermocline layer, the competition between the SSHPG and the density pressure gradient (DPG) determines the transition. During the transition, the amplitudes of the SSHPG and DPG are basically equivalent. The SSHPG needs time to develop sufficiently larger than the DPG. Therefore, the transition in the deeper layer significantly lags that in the shallower layer. The reversal of the SSHPG is mainly attributed to the change in the basin-scale wind stress curl over the southern SCS. The change in the DPG is mainly associated with the cooling of the water along the western continental slope, which is induced by upwelling. In case 2, there is no cooling along the western continental slope, and then the amplitude of the DPG is always far smaller than that of the SSHPG. Responding to the change in the SSHPG, the southern SCS WBC transition behaves consistently at full depth. Significance Statement: We have a comprehensive understanding of the South China Sea (SCS) circulation patterns in winter and summer. However, their seasonal transitions remain unclear, and a better understanding of them is potentially helpful for improving ocean circulation modeling and prediction. This paper focuses on the winter–summer transition in the SCS western boundary current (WBC). Above the thermocline (∼100 m), the transition behaves consistently in the vertical direction and is controlled by the conversion of the sea surface height–induced pressure gradient. Below the thermocline, the transition in the deeper layer of the WBC significantly lags that in the shallower layer of the WBC, which is associated with the competition between the SSH-induced pressure gradient and the density-induced pressure gradient at the sea surface. [ABSTRACT FROM AUTHOR]

When a wave breaks, it produces bubbles whose sizes depend on the breaking severity. This paper attempts to estimate wave breaking dissipation through a passive acoustic method. Initially, regular waves were forced to break in a flume. The breaking energy loss (severity) and the underwater acoustic noise were recorded. Two kinds of thresholds, in terms of sound wave amplitude and the ratio of sound wave height to period, respectively, were used together to identify the sound waves generated by newly formed bubbles. The frequencies of these sound waves are connected with the bubble sizes. Thus, a relationship between the mean bubble radius and the breaking severity was established and found to be linear. This laboratory relationship was then applied to Lake George data to study the breaking dissipation rate across the spectrum. An average acoustic spectral density threshold was proposed to identify breaking events from acoustic records in the field. The sound waves associated with bubble formation were selected by means of the same two kinds of threshold as used in the laboratory. Thus, the mean bubble radius of each breaking event was obtained and translated into the breaking severity. The values of experimental dissipation were compared with previous relevant results obtained through different methods as well as the wave breaking dissipation source terms ST6 (WAVEWATCH-III model) and are in good agreement with both of them. [ABSTRACT FROM AUTHOR]

Oceanic flows are energetically dominated by low vertical modes. However, disturbances in the form of atmospheric storms, eddy interactions with various forms of boundaries, or spontaneous emission by coherent structures can generate weak high-baroclinic modes. The feedback of the low-energy high-baroclinic modes on large-scale energetically dominant low modes may be weak or strong depending on the flow Rossby number. In this paper we study this interaction using an idealized setup by constraining the flow dynamics to a high-energy barotropic mode and a single low-energy high-baroclinic mode. Our investigation points out that at low Rossby numbers the barotropic flow organizes into large-scale coherent vortices via an inverse energy flux while the baroclinic flow accumulates predominantly in anticyclonic barotropic vortices. In contrast, with increasing Rossby number, the baroclinic flow catalyzes a forward flux of barotropic energy. The barotropic coherent vortices decrease in size and number, with a strong preference for cyclonic coherent vortices at higher Rossby numbers. On partitioning the flow domain into strain-dominant and vorticity-dominant regions based on the barotropic flow, we find that at higher Rossby numbers baroclinic flow accumulates in strain-dominant regions, away from vortex cores. Additionally, a major fraction of the forward energy flux of the flow takes place in strain-dominant regions. Overall, one of the key outcomes of this study is the finding that even a low-energy high-baroclinic flow can deplete and dissipate large-scale coherent structures at O(1) Rossby numbers. [ABSTRACT FROM AUTHOR]

The paper presents a combined numerical–deep learning (DL) approach for improving wind and wave forecasting. First, a DL model is trained to improve wind velocity forecasts by using past reanalysis data. The improved wind forecasts are used as forcing in a numerical wave forecasting model. This novel approach, used to combine physics-based and data-driven models, was tested over the Mediterranean. The correction to the wind forecast resulted in ∼10% RMSE improvement in both wind velocity and wave height over reanalysis data. This significant improvement is even more substantial at the Aegean Sea when Etesian winds are dominant, improving wave height forecasts by over 35%. The additional computational costs of the DL model are negligible compared to the costs of either the atmospheric or wave numerical model by itself. This work has the potential to greatly improve the wind and wave forecasting models used nowadays by tailoring models to localized seasonal conditions, at negligible additional computational costs. Significance Statement: Wind and wave forecasting models solve a set of complicated physical equations. Improving forecasting accuracy is usually achieved by using a higher-resolution, empirical coefficients calibration or better physical formulations. However, measurements are rarely used directly to achieve better forecasts, as their assimilation can prove difficult. The presented work bridges this gap by using a data-driven deep learning model to improve wind forecasting accuracy, and the resulting wave forecasting. Testing over the Mediterranean Sea resulted in ∼10% RMSE improvement. Inspecting the Aegean Sea when the Etesian wind is dominant shows an outstanding 35% improvement. This approach has the potential to improve the operational atmospheric and wave forecasting models used nowadays by tailoring models to localized seasonal conditions, at negligible computational costs. [ABSTRACT FROM AUTHOR]

The paper investigates switches of circulation orientation in inland basins, either at the surface or near the bottom. The study is based on an analytical 2D model used to simulate thermohaline circulation in lakes and inland seas. The model allows different density profiles varying in both horizontal and vertical directions. By assuming some simplifications (such as steady state, vanishing of an alongshore variability, and flat bottom), we are able to obtain an explicit expression of the circulation in the central transverse section of an elongated basin. Starting from three typical density profiles (bottom dense water, surface light water, and a combination of the two), the model reveals different circulation types (cyclonic and anticyclonic surface circulation, either prevailing along the whole vertical column or accompanied by an opposite circulation in the bottom layer). In addition, we analyze the impact of friction coefficients and basin dimensions on the switch from one circulation type to another. The simplified assumptions turn out not to be limiting, as other studies have shown that they do not change the main flow characteristics. More importantly, the results obtained are in keeping with empirical findings, numerical simulations, and physical experiments studied elsewhere. [ABSTRACT FROM AUTHOR]

Large-amplitude [±100 Sv (1 Sv ≡ 106 m3 s−1)], high-frequency oscillations in the Pacific Ocean's meridional overturning circulation within 10° of the equator have been found in integrations of the NEMO ocean general circulation model. Part I of this paper showed that these oscillations are dominated by two bands of frequencies with periods close to 4 and 10 days and that they are driven by the winds within about 10° of the equator. This part shows that the oscillations can be well simulated by small-amplitude, wind-driven motions on a horizontally uniform, stably stratified state of rest. Its main novelty is that, by focusing on the zonally integrated linearized equations, it presents solutions for the motions in a basin with sloping side boundaries. The solutions are found using vertical normal modes and equatorial meridional modes representing Yanai and inertia–gravity waves. Simulations of 16-day-long segments of the time series for the Pacific of each of the first three meridional and vertical modes (nine modes in all) capture between 85% and 95% of the variance of matching time series segments diagnosed from the NEMO integrations. The best agreement is obtained by driving the solutions with the full wind forcing and the full pressure forces on the bathymetry. Similar results are obtained for the corresponding modes in the Atlantic and Indian Oceans. Slower variations in the same meridional and vertical modes of the MOC are also shown to be well simulated by a quasi-stationary solution driven by zonal wind and pressure forces. [ABSTRACT FROM AUTHOR]

Concentrated poleward flows near the eastern boundaries between 2- and 4-km depth have been observed repeatedly, particularly in the Southern Hemisphere. These deep eastern boundary currents (DEBCs) play an important role in setting the large-scale tracer distribution and have nonnegligible contribution to global transports of mass, heat, and tracers, but their dynamics are not well understood. In this paper, we first demonstrate the significant role of DEBCs in the southeastern Atlantic, Indian, and Pacific Oceans, using the Southern Ocean State Estimate (SOSE) data assimilating product, and using high-resolution regional general circulation model configurations. The vorticity balances of these DEBCs reveal that, over most of the width of such currents, they are in an interior-like vorticity budget, with the meridional advection of planetary vorticity by and vortex stretching fwz being the largest two terms, and with contributions of nonlinearity and friction that are of smaller spatial scale. The stretching is shown, using a temperature budget, to be largely forced by resolved or parameterized eddy temperature transport. Strongly decaying signals from the eastern boundary in friction and stretching form the dominant balance in a sublayer close to the eastern boundary. The temporal variability of DEBCs is then examined, to help to interpret observations that tend to be sporadic in both time and space. The probability distribution functions of northward velocity inDEBCregions are broad, implying that flow reversals are common. Although the regions of the simulated DEBCs are generally local minima of eddy kinetic energy, they are still constantly releasing westward-propagating Rossby waves. [ABSTRACT FROM AUTHOR]

Along-track wavenumber spectral densities of sea surface height (SSH) are estimated from Jason-2 altimetry data as a function of spatial location and calendar month to understand the seasonality of meso- and submesoscale balanced dynamics across the global ocean. Regions with significant mode-1 and mode-2 baroclinic tides are rejected, restricting the analysis to the extratropics. Where balanced motion dominates, the SSH spectral density is averaged over all pass segments in a region for each calendar month and is fit to a four-parameter model consisting of a flat plateau at low wavenumbers, a transition at wavenumber k0 to a red power law spectrum k−s, and a white spectrum at high wavenumbers that models the altimeter noise. The monthly time series of the model parameters are compared to the evolution of the mixed layer. The annual mode of the spectral slope s reaches a minimum after the mixed layer deepens, and the annual mode of the bandpassed kinetic energy in the ranges [2k0, 4k0] and [k0, 2k0] peak ∼2 and ∼4 months, respectively, after the maximum of the annual mode of the mixed layer depth. This analysis is consistent with an energization of the submesoscale by a winter mixed layer instability followed by an inverse cascade of kinetic energy to the mesoscale, in agreement with prior modeling studies and in situ measurements. These results are compared to prior modeling, in situ, and satellite investigations of specific regions and are broadly consistent with them within measurement uncertainties. Significance Statement: This paper uses satellite observations to understand the source of ocean dynamics at the 1–100-km scales at which vertical motion becomes important and which are thus relevant for biology and for the exchange of heat and carbon with the atmosphere. The observations are consistent with a seasonal variation of dynamics at these scales, predicted by a specific theory of upper-ocean turbulence and confirmed by modeling studies and regional observations. We update prior satellite-based studies by excluding regions with competing effects, by our treatment of the noise, and by our characterization of the seasonality. This work provides a template for analyzing data from the upcoming Surface Water and Ocean Topography (SWOT) satellite. [ABSTRACT FROM AUTHOR]

The impacts of rainy days (>24 mm) on the physics of the surface atmosphere and upper ocean are characterized in the central Pacific Ocean (140°–170°W) on the equator, where deep-cycle turbulence substantially influences the sea surface temperature and air–sea heat flux on diurnal and longer time scales. Here, rainfall is relatively weak on average (1–3 mm day−1), and enough rain to substantially alter the diurnal cycle of upper-ocean buoyancy only occurs on the order of once in 100 days, albeit more frequently to the west and during El Niño and boreal winter. Rainy days are associated with multiple systematic changes in the surface atmosphere, but the freshwater and the reduction in daily downwelling shortwave radiation (by ∼50 W m−2) are codominant and drive systematic changes in the ocean during and the day after the rainy day. These two drivers explain ensemble average reductions in the upper-ocean salinity (−0.12 psu at 1 m) and temperature (−0.16°C at 1 m) and increases in buoyancy (+0.0005 m s−2 at 1 m), which are typically confined to a shallow fresh/warm mixing layer on the order of 10 m thick in the daytime. At deeper depths, the intrinsic ocean temperature, salinity, and velocity variability make it challenging to extract an ensemble average response to rainy days in observations, but some examples from observations and large-eddy simulations suggest that rainfall can significantly reduce the vertical extent and heat flux in the deep-cycle turbulence, although the bulk energetics and buoyancy flux of the turbulence are not necessarily modified by rain. Significance Statement: Rain significantly impacts social and ecological systems in many ways that are readily apparent in populated areas, but the impacts of rain over the ocean are not as well known. In this paper, sustained in situ observations over decades and highly resolved numerical simulations of ocean turbulence during a few rain events are used to characterize the impacts of rainy days on the surface–atmosphere and upper-ocean physics in the center of action of El Niño in the central equatorial Pacific. These results contribute to broader efforts to observe, understand, and accurately model the surface atmosphere, the upper ocean, and air–sea interaction in the central Pacific and thereby improve long-range weather and climate observations and predictions. [ABSTRACT FROM AUTHOR]

This paper introduces a new method for finding the top of thermocline (TTD) and halocline (THD) depths that may become a powerful tool for applications in shallow marine basins around the world. The method calculates the moving average of the ocean vertical profile's short-scale spatial variability (standard deviation) and then processes it to determine the potential depth at which temperature or salinity rapidly changes. The method has been calibrated using an extensive set of data from the ecohydrodynamic model EcoFish. As a result of the calibration, the values of the input parameters that allowed the correct determination of TTD and THD were established. It was confirmed by the validation carried out on the in situ profiles collected by the research vessel S/Y Oceania during statutory cruises in the southern Baltic Sea. The "MovSTD" algorithm was then used to analyze the seasonal variability of the vertical structure of the waters in Gdańsk Deep for temperature and salinity. The thermocline deepening speed was also estimated in the region analyzed. [ABSTRACT FROM AUTHOR]

There exist different theories representing the effects of surface gravity waves on oceanic flow fields. In the past, the author has conjectured that the vertically integrated, two-dimensional fluid equations of motion put forward by Longuet-Higgins and Stewart are correct and that theories that differ from their theory cannot be entirely correct; this paper explores these differences. Longuet-Higgins and Stewart deduced vertically integrated, two-dimensional equations featuring a wave radiation stress term in the fluid dynamic, momentum equation. More recently, the author has proposed vertically dependent, three-dimensional equations that have required correction but when vertically integrated, agreed with the earlier, two-dimensional equations. This paper derives both vertically independent and vertically dependent equations from the same base and, importantly, using the same expression for pressure in the belief that the paper will contribute to the understanding and clarification of this seemingly difficult topic in ocean dynamics. An error in the classical papers by Longuet-Higgins and Stewart has been detected. Although the final phase-averaged result was correct, the error has had consequences in the development of vertically dependent equations. The prognostic equations in this paper are for the Eulerian current plus Stokes drift; toward the end of the paper these equations are contrasted with prognostic equations for the Eulerian current alone. [ABSTRACT FROM AUTHOR]

This paper investigates the average shape of the largest waves arising in finite water depths. Specifically, the largest waves recorded in time histories of the water surface elevation at a single point have been examined. These are compared to commonly applied theories in engineering and oceanographic practice. To achieve this both field observations and a new set of laboratory measurements are considered. The latter concern long random simulations of directionally spread sea states generated using realistic Joint North Sea Wave Project (JONSWAP) frequency spectra. It is shown that approximations related to the linear theory of quasi-determinism (QD) cannot describe some key characteristics of the largest waves. While second-order corrections to the QD predictions provide an improvement, key effects arising in very steep or shallow water sea states are not captured. While studies involving idealized wave groups have demonstrated significant changes arising as a result of higher-order nonlinear wave–wave interactions, these have not been observed in random sea states. The present paper addresses this discrepancy by decomposing random wave measurements into separate populations of breaking and nonbreaking waves. The characteristics of average wave shapes in the two populations are examined and their key differences discussed. These explain the mismatch between findings in earlier random and deterministic wave studies. [ABSTRACT FROM AUTHOR]

The water mass transformation (WMT) framework describes how water of one class, such as a discrete interval of density, is converted into another class via air-sea fluxes or interior mixing processes. This paper investigates how this process is modified at the surface when mesoscale ocean eddies are present, using a state-of-the-art high-resolution climate model with reasonable fidelity in the Southern Ocean. The method employed is to coarse-grain the high-resolution model fields to remove eddy signatures, and compare the results with those from the full model fields. This method shows that eddies reduced the WMT by 2-4 Sv (10%-20%; 1 Sv ≡ 106 m³ s-1) over a wide range of densities, from typical values of 20 Sv in the smoothed case. The corresponding water mass formation was reduced by 40%at one particular density increment, namely, between 1026.4 and 1026.5 kg m-3, which corresponds to the lighter end of the range of Indian Ocean ModeWater in the model. The effect of eddies on surfaceWMT is decomposed into three terms: direct modulation of the density outcrops, then indirectly, by modifying the air-sea density flux, and the combined effect of the two, akin to a covariance. It is found that the first and third terms dominate, i.e., smoothing the outcrops alone has a significant effect, as does the combination of smoothing both outcrops and density flux distributions, but smoothing density flux fields alone has little effect. Results from the coarse-graining method are compared to an alternative approach of temporally averaging the data. Implications for climate model resolution are also discussed. [ABSTRACT FROM AUTHOR]

Wind-wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity functions, the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interpreted as the wave energy evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave-age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind-wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measured and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake. Significance Statement: This paper presents a growth function and spectrum model to describe wind-wave development in all water depths. Their applicability covers a wide range of wind forcing conditions including steady, accelerating, decelerating, and tropical cyclone events. Support for the unified spectrum model and growth function is presented with field observations and numerical computations. [ABSTRACT FROM AUTHOR]

Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving the wave-averaged equations using a large-eddy simulation method. The ocean fluid is driven by combined effects of wind stress, surface wave, and a steady current in the presence of stable vertical stratification. The resulting flow consists of two overlapping boundary layers, i.e., surface and bottom boundary layers, separated by an interior stratification. The overlapping boundary layers evolve through three phases, i.e., a rapid deepening, an oscillatory equilibrium and a prompt merger, separated by two transitions. Before the merger, internal waves are observed in the stratified layer, and they are excited mainly by Langmuir turbulence in the surface boundary layer. These waves induce a clear modulation on the bottom-generated turbulence, facilitating the interaction between the surface and bottom boundary layers. After the merger, the Langmuir circulations originally confined to the surface layer are found to grow in size and extend down to the sea bottom (even though the surface waves do not feel the bottom), reminiscent of the well-organized Langmuir supercells. These full-depth Langmuir circulations promote the vertical mixing and enhance the bottom shear, leading to a significant enhancement of turbulence levels in the vertical column. [ABSTRACT FROM AUTHOR]

The comments of Ardhuin et al. concerning the papers by Mellor from 2003 and 2015 are reviewed. It is found that the comments do not impact the validity of these papers. [ABSTRACT FROM AUTHOR]

Realistic, submesoscale-resolving numerical simulations are used to characterize the flow's statistics and the geography of surface submesoscale currents in the northern Gulf of Mexico. This study examines the role of the Mississippi-Atchafalaya River system in driving submesoscale currents during winter and summer, on and off the shelf, by investigating two sets of statistically equilibrated solutions, with and without river forcing. In this paper, the first of three, the authors analyze vorticity ζ, horizontal divergence δ, and available potential energy to eddy kinetic energy conversion and show that river forcing has an important effect on the spatial distribution and magnitudes of submesoscale currents in both seasons. During winter, solutions without river forcing display an increase in seasonal-mean values of ζ, δ and compared to solutions with river forcing, particularly east of the Mississippi River delta and offshore. On the contrary, during summer, seasonal-mean values are larger in solutions with river forcing throughout the entire region. The river effects can be rationalized in terms of scaling arguments that relate submesoscale current magnitudes to the surface boundary layer depth and lateral buoyancy gradients. River outflow enhances submesoscale currents by increasing lateral buoyancy gradients but suppresses them by decreasing the boundary layer depth. A discussion of the submesoscale-generating mechanisms that in each season may determine whether the enhancement effect overcomes the suppression effect or vice versa is presented. Regional comparisons of horizontal velocity spectra, root-mean-square ζ, root-mean-square δ, and root-mean-square across different resolutions show no sign of convergence even at 150-m horizontal resolution. This demonstrates the numerical challenge of modeling the full range of submesoscale currents. [ABSTRACT FROM AUTHOR]

The "bag breakup" fragmentation is the dominant mechanism for spume droplet production in high winds, which substantially affects the ocean–atmosphere exchange processes. The amount of droplets ejected from the surface, as well as their typical sizes, is prescribed by the surface wind velocity and fetch. The corresponding empirical correlations were obtained only for the limited parameters of the laboratory environment. The applicability range can be extended through the construction of a theoretical model that describes the initiation of the bag-breakup fragmentation, estimates the fragmenting liquid volume prescribing the droplet sizes, and determines the dependence on the wind parameters. This paper presents such a model. First, we conducted linear stability analysis of small-scale disturbances at the water surface under a high wind; this showed that the small-scale ripples (about 1 cm) propagating against the wind in the surface wind drift following the reference frame grew fast due to the Kelvin–Helmholtz instability, when the wind friction velocity u * exceeded the threshold of about 1 m s−1. Given the weak dispersion, the nonlinear stage of evolution was addressed using the Riemann simple wave equation modified to describe the increasing disturbances. The analytical solution for the equation suggested the scaling of the volume of liquid undergoing the bag-breakup fragmentation and its dependence on u * in agreement with the laboratory data. Using the scaling, we calculated the statistics of the bag-breakup fragmentation based on the lognormal size distribution of the fragmenting objects. Significance Statement: The "bag breakup" fragmentation is the dominant mechanism for generating spray in hurricane winds. The parameters of spray droplets substantially affect the exchange processes between the ocean and the atmosphere and, thereby, the development of sea storms. The rapid process of spray generation can only be studied in laboratory environments using sophisticated experimental techniques. To apply the laboratory data to field conditions, we need a theoretical model that describes the threshold for fragmentation initiation, the fragmenting liquid volume, which scales the size and number of spray droplets, their dependence on wind parameters, etc. In the present work, we suggest a simple analytical model of the bag-breakup initiation, verify it in the laboratory experiment, and suggest the statistical description of the fragmentation events. [ABSTRACT FROM AUTHOR]

The present study investigates the interannual variability of the tropical Indian Ocean (IO) based on the transfer routes of wave energy in a set of 61-yr hindcast experiments using a linear ocean model. To understand the basic feature of the IO dipole mode, this paper focuses on the 1994 pure positive event. Two sets of westward transfer episodes in the energy flux associated with Rossby waves (RWs) are identified along the equator during 1994. One set represents the same phase speed as the linear theory of equatorial RWs, while the other set is slightly slower than the theoretical phase speed. The first set originates from the reflection of equatorial Kelvin waves at the eastern boundary of the IO. On the other hand, the second set is found to be associated with off-equatorial RWs generated by southeasterly winds in the southeastern IO, which may account for the appearance of the slower group velocity. A combined empirical orthogonal function (EOF) analysis of energy-flux streamfunction and potential reveals the intense westward signals of energy flux are attributed to off-equatorial RWs associated with predominant wind input in the southeastern IO corresponding to the positive IO dipole event. Significance Statement: The present study gains a new insight into the mechanism of the Indian Ocean dipole events using a new diagnostic scheme for wave energy based on 61-yr hindcast experiments. The results have shown the existence of two sets of westward transfer of wave energy at the equator during 1994. One set of westward signals shows the same group velocity with theoretical equatorial Rossby waves that appear reasonably along the equator. The other set of westward signals at the equator represents a slightly slower group velocity than the theoretical equatorial Rossby waves, which is associated with abnormally extended southeasterly winds during the Indian Ocean dipole event. [ABSTRACT FROM AUTHOR]

The results of the subject paper are reviewed wherein credible Langmuir cells are produced by a numerical solution of the primitive fluid dynamic equations with a free surface. Whereas it is a major achievement, the claim that the same results support the general application of the so-called vortex force equations is challenged. [ABSTRACT FROM AUTHOR]

In regards to the recent paper by Pedlosky and Spall ( Journal of Physical Oceanography, November 2015), this comment maintains that the steady-state solutions of Rossby waves in a uniform eastward current past an island have waves on the upstream side that are not caused by the island because of inappropriate boundary conditions and the assumed form of the solution. The solutions are interesting but are not the solutions to the problem as posed in their paper. Similar upstream waves in a time-dependent numerical model are also inconsistent with linear Rossby wave theory, though the reasons for their presence are uncertain. [ABSTRACT FROM AUTHOR]

The intensity of tropical cyclones is sensitive to the air–sea fluxes of enthalpy and momentum. Sea spray plays a critical role in mediating enthalpy and momentum fluxes over the ocean's surface at high wind speeds, and parameterizing the influence of sea spray is a crucial component of any air–sea interaction scheme used for the high wind regime where sea spray is ubiquitous. Many studies have proposed parameterizations of air–sea flux that incorporate the microphysics of sea spray evaporation and the mechanics of sea spray stress. Unfortunately, there is not yet a consensus on which parameterization best represents air–sea exchange in tropical cyclones, and the different proposed parameterizations can yield substantially different tropical cyclone intensities. This paper seeks to review the developments in parameterizations of the sea spray–mediated enthalpy and momentum fluxes for the high wind speed regime and to synthesize key findings that are common across many investigations. [ABSTRACT FROM AUTHOR]