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The (2+1)-dimensional interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis is described by the space-time fractional Calogero-Degasperis (CD) and fractional potential Kadomstev-Petviashvili (PKP) equation. It can be modeled according to the Hamiltonian structure, the lax pair with the non-isospectral problem, and the pain level property. The proposed equations are widely used in beachfront ocean and coastal engineering to describe the propagation of shallow-water waves, demonstrate the propagation of waves in dissipative and nonlinear media, and reveal the propagation of waves in dissipative and nonlinear media. In this paper, we have established further exact solutions to the nonlinear fractional partial differential equation (NLFPDEs), namely the space-time fractional CD and fractional PKP equations using the modified Rieman-Liouville fractional derivative of Jumarie through the two variable ( G ′ / G , 1 / G )-expansion method. As far as trigonometric, hyperbolic, and rational function solutions containing parameters are concerned, solutions are acquired when unique characteristics are assigned to the parameters. Subsequently, the solitary wave solutions are generated from the solutions of the traveling wave. It is important to observe that this method is a realistic, convenient, well-organized, and ground-breaking strategy for solving various types of NLFPDEs.

Four oceanographic moorings were deployed across the South China Sea continental slope near 21.85∘ N, 117.71∘ E, from 30 May to 18 July 2014​​​​​​​ for the purpose of observing high-frequency nonlinear internal waves (NLIWs) as they shoaled across a rough, gently sloping bottom. Individual waves required just 2 h to traverse the array and could thus easily be tracked from mooring to mooring. In general, the amplitude of the incoming NLIWs tracked the fortnightly tidal envelope in the Luzon Strait; they lagged by 48.5 h and were smaller than the waves previously observed to the southwest near the Dongsha Plateau. Two types of waves, a waves and b waves,​​​​​​​ were observed, with the b waves always leading the a waves by 6–8 h. Most of the NLIWs were remotely generated, but a few of the b waves formed locally via convergence and breaking at the leading edge of the upslope-propagating internal tide. Waves incident upon the moored array with amplitude less than 50 m and energy less than 100 MJ m−1 propagated adiabatically upslope with little change of form. Larger waves formed packets via wave dispersion. For the larger waves, the kinetic energy flux decreased sharply upslope between 342 and 266 m, while the potential energy flux increased slightly, causing an increasing ratio of potential-to-kinetic energy as the waves shoaled. None of the waves met the criteria for convective breaking. The results are in rough agreement with recent theory and numerical simulations of shoaling waves.

The Gardner’s equation is the generalization of Kortweg-de Vries equation and modified Kortweg-de Vries equation having real life applications in different fields of science, such as, hydrodynamics, quantum field theory, etc. Moreover, it has applications in fluid mechanics where it explains surface and internal waves. This manuscript addresses application of the new ϕ 6 -model expansion method to Gardner’s equation for getting its solitary wave solutions. Such new results aid in getting noteworthy advances in various disciplines of science and technology. Periodic, kink, anti-kink, bright, dark, w-shaped and singular soliton solutions of the governing equation have been constructed. The proposed method takes into account a variety of closed form solutions using the Jacobi elliptic functions. The graphical illustration of some of the obtained solutions has been presented for a suitable choice of free parameters to depict the dynamic nature of the obtained wave solutions.

Upcoming satellite missions will observe the sea surface height (SSH) fields at a very high spatial resolution, which has generated an urgent need to understand better how well geostrophy can represent the ocean current field at finer scales, particularly in coastal regions characterized by complex flow geometry. We conduct statistical and spectral analyses of high-resolution surface currents and SSHs off the Oregon coast to examine the relative contribution of geostrophy and ageostrophy in coastal ocean currents. We analyze forward numerical simulations based primarily on a regional ocean model (ROMS) and use regional observations of high-frequency radar (HFR)-derived surface currents and altimeter-derived geostrophic currents and a subset of global domain numerical simulations (MITgcm) as secondary resources. Regional submesoscale ageostrophic currents account for up to 50% of the total variance and are primarily associated with near-inertial currents and internal tides. Geostrophy becomes dominant at time scales longer than 3 to 10 days and at spatial scales longer than 50 km, and is dependent on the depth and distance from the coast in the cross-shore direction. Ageostrophy dominates in the near-inertial and super-inertial frequency bands, which correspond to near-inertial motions (Coriolis force dominates) and high-frequency internal waves/tides (pressure gradient dominates), respectively. Because of ageostrophy, it may not be possible to estimate submesoscale currents from SSHs obtained from upcoming satellite missions using the geostrophic relationship. Thus, other concurrent high-resolution in-situ observations such as HFR-derived surface currents, together with data assimilation techniques, should be used for constructive data integration to resolve submesoscale currents.

In this study, a three-dimensional internal wave (IW)—cylinder—terrain coupled numerical model is established. Based on the large-eddy simulation (LES) method, the IW mechanical characteristics of the cylinder and the flow field evolution around the cylinder over different types of terrains are explored. The similarities and differences in the mechanical characteristics of the cylinders in the environments with and without terrains are compared. The research results show that, when the IWs propagate over terrain, the waveform structures are prone to continuous changes. The intense reverse alternating flow of the upper and the lower water, bounded by the pycnocline, results in huge IWs forces differences between the case without terrains and the cases with terrains. In the case without terrains, the maximum horizontal resultant force on the cylinder is positive, while the resultant forces are negative in the cases with terrain. Compared with the case without terrain, the shallow-water effect caused by the combined action of the terrain and the IWs enhances the flow field strength, making the lower parts of the cylinder suffer larger horizontal forces in the opposite direction to the IW direction. Moreover, the additional vortices produced by the interaction between the IWs and the terrain causes a more complex flow field around the cylinder and the greater forces on the cylinder.

Theoretically, propagating internal tides in the ocean may reflect at turning depths, where buoyancy frequencies equal tidal frequencies, before colliding with the air-sea interface or rugged bottom topography. Globally, the internal tide lower turning depths (ITLTDs) in the open ocean have been mapped; however, knowledge of the presence of ITLTDs in the South China Sea (SCS) is lacking. In this study, 2 125 high-quality temperature-salinity profiles (including 58 deep-sea hydrographic measurements with observational depths exceeding 3 000 m) are collected and analyzed to investigate the existence of ITLTDs in the SCS. Furthermore, the concept of the upper turning depth is first introduced in the context of internal tides, and internal tide upper turning depths (ITUTDs) are also investigated. ITLTDs are found to exist at several abyssal stations; these stations are distributed mostly in the southern part of the SCS basin, possibly due to the greater water depths there. Fewer locations show the presence of ITLTDs for K1 versus M2 tidal frequencies because of the lower tidal frequency. The distance between ITLTDs and the seafloor ranged from 270 m to more than 1 200 m, implying the possible existence of multiple internal wave evanescent regions in the abyssal bottom. ITUTDs of tens of meters are ubiquitous in the SCS; stations with the presence of ITUTDs are located mainly in the northeastern SCS due to the intensive observations there. However, the calculated ITUTDs have large uncertainties; they are sensitive to the selected bin values. The horizontal propagation directions of internal tides in the SCS change dramatically, and as a result, the estimated turning depths under the full Coriolis force definition are different compared to that under the traditional approximation.

Ocean surface sunglint reflection is very important for detecting ocean surface roughness, oil spills, oceanic internal waves, and so on. Although statistical sunglint models (i.e., Cox-Munk model) have been used successfully on coarse-resolution spaceborne optical images for several decades, it is still a challenge to apply it to high spatial resolution images due to scale effects of the optical remote sensing. In this study, a sea wave model and the Pinhole camera model were employed to simulate the sunglint reflection images with different spatial resolutions and viewing angles. Coefficient of variation (CV) of sunglint reflection collected from various images indicates that there is uncertainty in sunglint reflection in images with different spatial resolutions. This study presents the applicability of sunglint statistical models in images with different spatial resolutions and viewing angles.

Significant current velocity near the sea bottom can be induced by internal waves, even for water a few hundred meters in depth. In this study, a nonhydrostatic ocean model was applied to simulate the generation and propagation of internal waves on the continental slope of the northern SCS. Based on the analyses of the vertical profiles of the currents, the propagation of internal waves along the continental slope can be categorized into six modes. The bed shear stress and the bedload transport were calculated to analyze the general characteristics of sediment transport along the continental slope of the northern SCS. Generally, there was no sediment transport on the sea bottom induced by the internal waves when the water depth was deeper than 650 m or shallower than 80 m. The downslope sediment transport dominated the slope at a water depth range of 200~650 m, while the upslope sediment transport dominated the slope at a water depth range of 80~200 m. The predicted directions of the bedload transport are coincident with the field observations of sand wave migration on the continental slope, which further confirms that the main cause of the generation and formation of sand waves on the continental slope of the northern SCS is the strong bottom current induced by the shoaling process of internal waves.

We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the pretense that the boundary at any collision point is either horizontal or vertical (relative to a predetermined direction representing gravity). These systems are point particle approximations for the motion of internal gravity waves in closed containers, hence the name. For a class of tables similar to rectangular trapezoids, but with the slanted leg replaced by a general curve with downward concavity, we prove that the dynamics has only three asymptotic regimes: (1) there exist a global attractor and a global repellor, which are periodic and might coincide; (2) there exists a beam of periodic trajectories, whose boundary (if any) comprises an attractor and a repellor for all the other trajectories; (3) all trajectories are dense (that is, the system is minimal). Furthermore, in the prominent case where the table is an actual trapezoid, we study the sets in parameter space relative to the three regimes. We prove in particular that the set for (1) has positive measure (giving a rigorous proof of the existence of Arnol'd tongues for internal-wave billiards), whereas the sets for (2) and (3) are non-empty but have measure zero., Comment: Final preprint for Nonlinearity, 29 pages, 11 figures

Temperature is used to trace ocean density variations, and reveals internal waves and turbulent motions in the deep ocean, called ‘internal motions.’ Ambient temperature detected by geophysical differential pressure gauges (DPGs) may provide year-long, complementary observations. Here, we use data from four DPGs fixed on the ocean bottom and a high-resolution temperature sensor (T-sensor) 13 m above the seafloor as a square-kilometer array deployed offshore ~ 50 km east of Taiwan facing the open Pacific Ocean to examine the impact of temperature on DPG signals related to internal motions. The DPG signals correlate with T-sensor temperature variations between 0.002 and 0.1 mHz, but have time shifts partially caused by slow thermal conduction from the ambient seafloor to the DPG chamber and partially by internal motion propagation time across the array. Applying beamforming-frequency-wavenumber analysis and linear regression to the arrayed T-sensor and DPG data, we estimate the propagating slowness of the internal motions to be between 0.5 and 7.4 s m−1 from the northwest and northeast quadrants of the array. The thermal relaxation time of the DPGs is within 103–104 s. This work shows that a systematic scan of DPG data at frequencies

This paper describes the results of studying the waves in the southern part of the Sea of Okhotsk on the sea routes between Sakhalin and Iturup islands by means of autonomous wave recorders. The study was performed in order to improve the safety of the maritime transport system and ensure its safe functioning. Analysis of the wave regime and weather conditions in the southern part of the Sea of Okhotsk, has shown that a cyclone of any direction approaching the southern part of the Sea of Okhotsk, causes sea waves with heights of more than 1.7 meters in the considered water area and nearshore of Iturup Island. However, if a cyclone approaches Sakhalin Island from the northwest direction, the height of wind waves and swell in the coastal area of the southeast of the island is small, and here is an opportunity for ships to take shelter from the storm. The analysis of long waves with tidal harmonic periods of 4 hours and more has shown, that they have almost the same oscillation phase for both islands. The internal waves caused by the local features of bathymetry and relief of the coastal zone for each adjacent water area are analyzed. Surface gravitational waves with a period of about 2.8 hours were detected at Kuibyshevsky and Kurilsky bays, and waves with a period of 2.4 hours were detected near the Okhotskoye village at Sakhalin Island. It is shown that the highest Q-factor in the Kurilsk region has the resonant water area for the periods of 4.5 minutes. It is noted that for these waves the phenomenon of a tyagun (harbour oscillations) can be expected during a storm at sea.

The settlement of intertidal barnacles Chthamalus spp. was measured for an entire recruitment season at 3 sites separated by 100 m in Baja California, Mexico. During a 10 d pulse that accounted for nearly 30% of yearly settlement, coastal wind speed and direction, nearshore water column temperature, and current velocities were also measured. During this period, strong internal tidal forcing was observed, with short episodes (1-1.5 h) of rapid fluctuations in water column temperature, stratification, and currents. Chthamalus spp. settlement was significantly and positively correlated with cumulative high-frequency fluctuations in temperature, thermal stratification, and surface current flows, but not with onshore winds. Furthermore, the spatial pattern in the number of settlers was correlated with the angle of propagation estimated for onshore-moving internal waves, potentially modulated by nearshore bathymetry. This relationship between Chthamalus spp. settlement and high-frequency changes in water column temperature was also shown for a site in La Jolla, California, USA, but not for a similar barnacle, Balanus glandula, suggesting that interspecific differences in larval behavior and nearshore depth distribution may translate into differences in transport. Our results suggest that both the number of settlers at shore and their spatial pattern can be modulated by the intensity and direction of internal wave events, at least during peak settlement periods. Future research should consider both the intensity and geometry of internal-wave-induced variability in the nearshore, as well the small-scale features of coastal geomorphology and bathymetry.

The development of ocean remote sensing makes it possible to obtain valuable information from a large amount of data. Deep learning is a powerful tool that is beneficial for obtaining ocean informa...

The generation of T waves in a deep ocean by an earthquake in its epicentral region is often observed, but the mechanism of the excitation of the acoustic waves travelling horizontally with the speed of sound remains controversial. Here, the hypothesis is investigated that the abyssal T waves are generated by the scattering of ballistic sound waves by surface and internal gravity waves in the ocean. Volume and surface scattering are studied theoretically in the small perturbation approximation. In the 3-50 Hz typical frequency range of the observed T waves, the linear internal waves are found to lack the necessary horizontal spatial scales to meet the Bragg scattering condition and contribute appreciably to the T-wave excitation. In contrast, the ocean surface roughness has the necessary spatial scales at typical sea states and wind speeds. The efficiency of the acoustic normal modes' excitation at surface scattering of the ballistic body waves by wind seas and sea swell is quantified and found to be comparable to that of the established mechanism of the T-wave generation at downslope conversion at the seamounts. The surface scattering mechanism is consistent with key observational features of the abyssal T waves, including their ubiquity, low-frequency cutoff, presence on seafloor sensors, and weak dependence on the earthquake focus depth.

The internal waves are different phenomenon in oceanography and these are also waves but occur in the inside of the ocean. Many techniques exist for the detection of internal waves but every method has its own advantages and drawbacks. Earth observations systems keep an eye in monitoring ocean internal waves at regular intervals of time. But automatic detection of internal waves is still a challenging problem. This paper proposes a method which gives complete methodology for internal wave detection. The method is divided into three main stages that are input data pre-processing, parameter extraction and modeling. The proposed system will initially take Synthetic Aperture Radar (SAR) images, pre-process for noise. Augmentation techniques such as flip and rotation resolve occlusion caused by clouds. U-Net is used for segmentation and feature extraction of wave parameters such as frequency, amplitude, longitude, latitude. Finally, for ocean internal wave modeling, KdV (Korteweg–de Vries) solver is used. KdV solver takes the internal wave parameters as input and it gives the velocity, density plots of internal waves. The deep learning model is tested on SAR images and proved to give accurate results for the internal wave detection.

This work deals with applying a rapidly convergent approximation method to obtain some (weak) nonsmooth solitary or periodic solutions of a generic version of the Korteweg-de Vries and the Benjamin-Bona-Mahony equations, the generalized Gardner equation with dual power-law nonlinearity. A novel approach has been adopted to derive conditions among parameters for which the obtained solution may be bounded. Explicit parameter dependence of few constants of the motion corresponding to the nonsmooth solitary or periodic solutions obtained here has been presented. Results derived here may be helpful in interpretations of large-amplitude internal waves in the ocean and for irregularly large-amplitude waves in other fields of nonlinear physics, e.g., optics and dusty- or magneto-plasmas.

Large amplitude internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. The Dubreil-Jacotin-Long, or DJL, theory of exact internal solitary waves can account for a background shear, doing so at a cost of algebraic complexity and a lack of a mathematical proof of algorithm convergence. Waves in the presence of shear that is strong enough to preclude theoretical calculations have been reported in observations. We report on high resolution simulations of stratified adjustment in the presence of strong shear currents. We find instances of large amplitude solitary-like waves with recirculating cores in parameter regimes for which DJL theory fails, and of wave types that are completely different in shape from classical internal solitary waves. Both are spontaneously generated from general initial conditions. Some of the waves observed are associated with critical layers, but others exhibit a propagation speed that is very near the background current maximum. As such they are not freely propagating solitary waves, and a DJL theory would not apply. We thus provide a partial reconciliation between observations and theory.

In this paper, we consider coupled Korteweg-de Vries equations that model the propagation of shallow water waves, ion-acoustic waves in plasmas, solitons, and nonlinear perturbations along internal surfaces between layers of different densities in stratified fluids, for example propagation of solitons of long internal waves in oceans. The method of Lie group analysis is used to on the system to obtain symmetry reductions. Soliton solutions are constructed by use of a linear combination of time and space translation symmetries. Furthermore, we compute conservation laws in two ways that is by multiplier method and by an application of new conservation theorem developed by Nail Ibragimov.

In this paper, a multiphase moving particle semi-implicit (MPS) method is developed by introduction of various multiphase models into the original MPS method for single-phase flows, and is then applied to the numerical simulations of two-layer-liquid and three-layer-liquid sloshing in a 2-D rectangular tank under different external excitations. To validate the accuracy of the present multiphase MPS method, the qualitative and quantitative results, including wave profiles, interface elevations and impact pressures, are compared with experimental data and other numerical results, which show a good agreement. In particular, the evolutions of free surface and phase interfaces are compared and an obvious discrepancy is found, indicating that the phase interfaces may suffer from complex deformations while the free surface keeps relatively quiet. Moreover, the different modes of phase interface are observed under different excitation frequencies. Then, the violent sloshing of a three-layer-liquid system is simulated and the phenomenon of internal wave breaking is well captured, which mainly benefitted from the Lagrangian basis of MPS method and its advantage in multiphase flows with complex interfaces. Finally, the three-layer-liquid sloshing with a vertical baffle are simulated to investigate the suppressing effect of baffle on multi-layer-liquid sloshing.

Internal waves generated by the movement of surface and subsurface vehicles in the ocean have specific importance in maritime applications. These types of waves are categorized as forced internal waves. In this article, an attempt using a novel optical method is made to study the forced internal waves that are generated by a large surface vehicle in a controlled sea exercise. The optical method uses a diode laser operating at 635 nm and a lateral-effect position-sensitive photodetector. The laser beam undergoes modulation in both its intensity and beam positions with respect to the density variations that are caused in the stratified ocean by the forced internal waves. The experimental scheme, the system aspect of the optical method, and supporting theoretical aspects are detailed with corroborating experimental results. It is observed that the frequency of the forced internal waves also remains within the band of naturally occurring ambient oscillations in the ocean. The obtained results indicate that the forced internal waves detected by the optical method can be used for detecting the movement of maritime vehicles in the ocean.

Fishes typically occupy a species-specific temperature range, with their occupied depth being related to the lake’s temperature profile. When a fish’s preferred temperature range coincides with the thermocline, the location of their preferred thermal habitat is influenced by the rise and fall of internal waves, leading to possible changes in fish depth. These internal waves are common in large, stratified lakes, yet we do not know how they affect the spatial distribution and behavior of freshwater fishes. We conducted nighttime hydroacoustic surveys in a large, deep embayment of a large thermally stratified lake to observe whether pelagic fish respond to vertical oscillations of the thermocline caused by internal waves. The coldwater pelagic fish in our study (primarily cisco, Coregonus artedi) typically occupied a narrow vertical band approximately 5–8 m thick and temperatures between 10.8 ± 0.8–13.6 ± 1.6 °C (fishes sized 106–500 mm), just below the thermocline (centered around 15–17 °C). Importantly, the upper bound of fish depth varied in response to vertical thermocline movements associated with internal waves, suggesting fish respond to changes in their physical environment on timescales commensurate with basin-scale internal wave periods (hours to days), to remain within their preferred thermal habitat. Dissolved-oxygen levels were typically above avoidance thresholds of these fish, thus not likely exerting a strong influence on fish location. Our findings emphasize the need to account for internal waves when designing hydroacoustic and netting surveys, as thermocline movements can influence where fish are located.

In this study, we diagnose the time variability and vertical structure of the high- and low-frequency motions on the Mississippi-Alabama Shelf as observed with a bottom-mounted ADCP (Acoustic Doppler Current Profiler) and CTD (Conductivity-Temperature-Depth). The mooring was deployed about 20 km offshore of Mobile Bay for a period from May 17 to August 23, 2018. At this latitude, the diurnal land and sea breeze has the same frequency as the local inertial frequency. Similar to the wind, the observed high-frequency baroclinic velocities (> 30 cm/s) have a broadband diurnal peak and more energy in the clockwise motions. About 60% of the variance in these motions is due to mode 1, which resembles a two-layer structure with surface and bottom velocities that are 180∘ out of phase. These are all characteristics of wind-driven motions that interact with the coastal wall. The month of June features the best conditions for energetic near-inertial motions: upwelling, consistent sea breeze, and a more continuous instead of a two-layer stratification. This causes near-inertial energy to be also projected on a baroclinic mode 2, featuring a subsurface maximum. This maximum may be attributed to the downward propagation of near-inertial internal wave energy. The observed alongshore low-frequency flows and the up- and downwelling are mostly driven by low-frequency winds. About 83% of the variance in the alongshore low-frequency flows is due to mode 1, which eigenfunction resembles a vertically sheared flow. We find that the amplitude of the near-inertial motions is modulated by the up- and downwelling. During downwelling, the near-inertial baroclinic kinetic energy is greatly reduced because of a reduction in stratification and weaker diurnal winds.

Internal solitary waves have been documented in several parts of the world. This paper intends to look at the effects of the variable topography and rotation on the evolution of the internal waves of depression. Here, the wave is considered to be propagating in a two-layer fluid system with the background topography is assumed to be rapidly and slowly varying. Therefore, the appropriate mathematical model to describe this situation is the variable-coefficient Ostrovsky equation. In particular, the study is interested in the transition of the internal solitary wave of depression when there is a polarity change under the influence of background rotation. The numerical results using the Pseudospectral method show that, over time, the internal solitary wave of elevation transforms into the internal solitary wave of depression as it propagates down a decreasing slope and changes its polarity. However, if the background rotation is considered, the internal solitary waves decompose and form a wave packet and its envelope amplitude decreases slowly due to the decreasing bottom surface. The numerical solutions show that the combination effect of variable topography and rotation when passing through the critical point affected the features and speed of the travelling solitary waves.

March 15, 2021 Chief Researcher, Head of the Laboratory of Hydrological Processes of the P.P. Shirshov Institute of Oceanology of the Russian Academy of Sciences, DSc, ex-president of the International Association for Physical Ocean Sciences (IAPSO) Evgeny Morozov is 75 years old. E.G. Morozov is a prominent scientist and organizer of world-class science in the field of studying the temporal and spatial variability of hydrological processes and internal waves in a wide range of scales. He was the first to build a map of the amplitudes of tidal internal waves of the World Ocean. His monograph “Oceanic Internal Waves” published in 1985 in Russian, as well as his article “Semidiurnal internal wave global field”, published in the Deep Sea Research in 1995, are among the most cited on the problem of internal tidal waves. Unique results were obtained by E.G. Morozov in the study of internal waves in the Arctic, including under the ice and near the front of glaciers sliding into the ocean on Spitsbergen. He made a significant contribution to the study of various currents: the Gulf Stream, the Kuroshio and their rings, the Antarctic Circumpolar Current, the California Current, the Falkland Current, the Lomonosov and Tareev subsurface equatorial currents. Since 1999 he has been a member of the Executive Committee of the International Association for the Physical Sciences of the Ocean (IAPSO) and since 2011 he has been elected President of the IAPSO, represented the IAPSO in this capacity on the Executive Committee of the International Geodetic and Geophysical Union (IUGG) and on the Executive Committee of the Scientific Committee on Oceanic research (SCOR). E.G. Morozov is the chairman of the Ocean Physical Sciences Section of the National Geophysical Committee of the Russian Academy of Sciences.

Energy for ocean turbulence is thought to be transferred from its presumed sources (viz., the mesoscale eddy field, near-inertial internal waves, and internal tides) to the internal wave continuum, and through the continuum via resonant triad interactions to breaking scales. To test these ideas, the level and variability of the oceanic internal gravity wave continuum spectrum are examined by computing time-dependent rotary spectra from a global database of 2260 current meter records deployed on 1362 separate moorings. Time series of energy in the continuum and the three “source bands” (near-inertial, tidal, and mesoscale) are computed, and their variability and covariability examined. Seasonal modulation of the continuum by factors of up to 5 is seen in the upper ocean, implicating wind-driven near-inertial waves as an important source. The time series of the continuum is found to correlate more strongly with the near-inertial peak than with the semidiurnal or mesoscale. The use of moored internal-wave kinetic energy frequency spectra as an alternate input to the traditional shear or strain wavenumber spectra in the Gregg–Henyey–Polzin finescale parameterization is explored and compared to traditional strain-based estimates.

Seawater temperature plays a key role in underwater acoustics and marine fishery, etc. In oceanographic surveys, it is often desirable to detect the temperature profile and obtain its spatio-temporal variation. The present study shows that the temperatures at the depths which are the three extreme points of the first two empirical orthogonal function (EOF) modes, contain the largest amount of information. Based on the back propagation (BP) neural network, a model for reconstructing the full-depth temperature profile using a few temperatures at fixed depth is established. The experimental result shows that the root mean square error (RMSE) of the temperature profile inversion in the test set is mostly less than 0.2 °C, and the three-dimensional temperature field obtained in this study is relatively reliable.

Internal waves with high vertical wavenumber structures on the northern part of the eastern ridge in Luzon Strait were investigated using shipboard observations and a wave propagation model. Detailed repeat observations across the ridge revealed complex undulations of isopycnals near the ridge that were characterized by vertically alternating concave and convex structures. In addition, strong eastward and westward flow areas with horizontal and vertical scales of 3–5 km and 150–250 m, respectively, occurred alternately on the downstream side of the ridge. These high-wavenumber structures in flow and density fields were associated with internal waves generated by interactions between diurnal tidal flow and the meridional submarine ridge in the strait; an acoustic Doppler current profiler recorded no signals of the Kuroshio Current and semi-diurnal tides in the zonal flow on the western slope of the eastern ridge. Many temperature inversions around the ridge exhibited vertical scales of predominantly ~ 30 m. Simple calculations of internal wave motion reveal that each internal wave mode tends to stagnate near the summits of the ridge depending on the direction and strength of the background tidal flow. This suggests that the observed high-wavenumber structure in the flow profiles near the ridge is ascribed to the superposition of transient internal wave modes, although this is not the main cause of the temperature inversions. As a possible mechanism to explain the temperature inversions, we propose that higher-mode internal waves emanating from the unresolved topographic undulations are trapped by the observed high-wavenumber structures, resulting in turbulent mixing.

A mechanism for the appearance of anomalous variations in the vertical component of the electric field strength recorded at the Mikhnevo Geophysical Observatory of Sadovskii Institute of Geosphere Dynamics, Russian Academy of Sciences, during strong remote earthquakes is proposed. It is shown that intensification of radon emanations in the observational area stimulated by the seismogravitational oscillations and subsequent modulation of radon and aerosol concentrations by atmospheric internal waves may result in these electric field variations.

Oceanic internal waves play a crucial role in ocean activities. Currently, the approach to detecting oceanic internal waves from synthetic aperture radar (SAR) images is becoming robust. To efficie...

Sonar performance prediction models require environmental inputs, including bottom depth and composition, sound-speed profile (SSP), and wave or wind conditions. Temporal and spatial variation and measurement uncertainties in environmental inputs result in uncertain model outputs. Ideally, acoustic fluctuations could be predicted from input parameter variability using a suitable modeling framework. A data set consisting of 460 SSPs and acoustic transmission loss (TL) measurements between 300 and 900 Hz was acquired during GLISTEN15, a 2015 Mediterranean Sea trial led by North Atlantic Treaty Organization's Centre for Maritime Research and Experimentation. The TL was measured in 5-min sampling periods at fixed source-to-receiver ranges of 0.5–10 km over two separate days. A gradual change in TL as large as 15 dB over 5 min was observed at some receivers and frequencies. Predicted TL variability was compared to measured TL variability by using the SSPs as inputs to an acoustic propagation model. Purely stochastic modeling either over- or underpredicted variability, depending on the temporal and spatial separation of the SSPs used as inputs. In this article, an internal wave model derived from the SSP time series was used to demonstrate the possible effect of internal waves propagating perpendicular to the source–receiver direction. The best agreement between modeled and measured variability was obtained for internal waves of 1536-s period and 0.8–1.6-m amplitude. In this way, an approach that included a physically plausible model of internal wave dynamics grounded in a few relevant in situ measurements provided good predictions of observed TL variability and a reasonable explanation of its origin.

The results of numerical simulation of interferometric processing of hydroacoustic information for two frequency ranges in the case where intense internal waves induce horizontal refraction of waves of a broadband-source field on a stationary path are presented and discussed. Two nonoverlapping spectral-density ranges are formed as a result of double Fourier transform of the interference pattern in the time–frequency domain. Filtering of these ranges and subjecting them to double inverse Fourier transform provides interference patterns of undisturbed and disturbed fields (i.e., patterns in the absence and in the presence of intense internal waves, respectively). The relative error in reconstructing the interference pattern of undisturbed field is estimated. Approaches to adaptation of the obtained results to the problems of underwater acoustic communication are proposed and outlined.

We present observations from deployments of a turbulent microstructure instrument and a CTD package in the northern South China Sea from April to May 2010. From these we determined the turbulent mixing (dissipation rate ε and diapycnal diffusivity κ), nutrients (phosphate, nitrate, and nitrite), nutrient fluxes, and chlorophyll a (Chl-a) in two transects (A and B). Transect A was located in region far away from the Luzon Strait where turbulent mixing in the upper 100 m was weak (κ~10−6–10−4 m2 s−1). Transect B was located in region near the Luzon Strait where the turbulent mixing in the upper 100 m was strong (κ~10−5–10−3 m2 s−1) due to the influence of the internal waves originating from the Luzon strait and the water intrusion from the western Pacific. In both transects, there was a thin subsurface chlorophyll maximum layer (SCML) (0.3–0.7 mg m−3) nested in the water column between ~50 and 100 m. The observations indicate that effects of turbulent mixing on the distributions of nutrient and Chl-a were different in different transects. In transect with weak turbulent mixing, nutrient fluxes induced by turbulent mixing transported nutrients to the SCML but not to the upper water. Nutrients were sufficient to maintain a local SCML phytoplankton population and the SCML remained compact. In transect with strong turbulent mixing, nutrient fluxes induced by turbulent mixing transported nutrients not only to the SCML but also to the upper water, which scatters the nutrients in the water column, and weakens and diffuses the SCML.

Because the flow direction of the water above and below the interface of internal wave is opposite, internal wave has a strong shear effect on ocean structures. A dynamic model of internal wave act...

—The hydrodynamic system that admits the development of internal wave attractors under biharmonic forcing is investigated. It is shown that in the case of low amplitude of external forcing the wave pattern consists of two attractors that interact between themselves only slightly: the total energy of the system is equal to the sum of energies of the components with high accuracy. In the nonlinear case the attractors interact in the more complex way which leads to the development of a cascade of triad interactions generating a rich set of time scales. In the case of closely adjacent frequencies of the components of a biharmonic perturbation, the nonlinear “beating” regime develops, namely, the mean energy of the system of coupled attractors performs oscillations at a large time scale that corresponds to the beating period. It is found that the high-frequency energy fluctuations corresponding to the same mean energy can differ by an order of magnitude depending on whether the envelope of the mean value increases or decreases.

Free internal waves in a two-dimensional vertically inhomogeneous stratified flow are considered in the Boussinesq approximation with account of the Earth’s rotation. The equation for the amplitude of the vertical velocity of a fixed mode of internal waves has complex coefficients; therefore, the eigenfunction and the wave frequency are complex. The imaginary part of frequency is small and can be both positive and negative. For this reason, both weak damping and weak strengthening of the wave are possible depending on the wavenumber and the mode number. The vertical wave momentum fluxes are nonzero and can be greater than the corresponding turbulent fluxes.

In the paper, we first present an exact solution for geophysical internal waves with centripetal forces and geophysical edge waves without centripetal forces in modified equatorial β -plane approximation. Then we apply the short-wavelength perturbation method to show an instability threshold for geophysical internal waves propagating eastward with centripetal forces and geophysical edge waves without centripetal forces in the modified equatorial β -plane approximation.

We use the Hamiltonian structure of equatorial wave-current interactions in the case of non-zero constant vorticity in the near-surface homogeneous layer, studying the dispersion relation for linear long waves outrunning the currents (downstream waves). We also investigate the behavior of the lifespan of the solution of the evolution equation for nonlinear long internal waves with respect to vorticity values.

Internal waves (IWs), observed in the world oceans, have significant impacts on ocean engineering and environments. In this study, we collected satellite images from Moderate-Resolution Imaging Spectroradiometer and Visible Infrared Imaging Radiometer Suite sensors in the Sulu-Celebes Sea from 2016 to 2019 to understand the IW generation and propagation. Satellite observations show a coherent IW phase difference in both seas, indicating that the IWs are alternatively generated when the tidal currents oscillate back and forth in the Sulu Archipelago, which separates two seas. A new generation site is found for occasionally observed long IWs in the eastern Sulu Sea. To understand the IW propagation characteristics, we developed a machine-learning-based forecast model. We trained the model with both IW wave crest curves extracted from satellite images and published climatological ocean temperature–salinity profiles. Since many satellite images contain IW packets generated at two or three tidal cycles, we can validate the model performance by matching the model prediction after one or two tidal cycles with the second or third wave crests in satellite images. Three factors are adopted to evaluate the forecast results: the root-mean-square error (RMSE), the Frechet distance (FD), and the correlation coefficient (CC). The forecast model has an average error with an RMSE of 12.92 km, an FD of 18.73 km, and a CC of 0.98. Analysis shows that a smaller time step is preferred in regions where the water depth changes significantly. Comparison with the Korteweg–de Vries equation solutions shows that the developed forecast model is more robust when errors introduced to the model inputs.

A method based on machine learning and image processing techniques has been developed to track the surface expression of internal waves in near–real time. X-band radar scans are first preprocessed and averaged to suppress surface wave clutter and enhance the signal-to-noise ratio of persistent backscatter features driven by gradients in surface currents. A machine learning algorithm utilizing a support vector machine (SVM) model is then used to classify whether or not the image contains an internal solitary wave (ISW) or internal tide bore (bore). The use of machine learning is found to allow rapid assessment of the large dataset, and provides insight on characterizing optimal environmental conditions to allow for radar illumination and detection of ISWs and bores. Radon transforms and local maxima detections are used to locate these features within images that are determined to contain an ISW or bore. The resulting time series of locations is used to create a map of propagation speed and direction that captures the spatiotemporal variability of the ISW or bore in the coastal environment. This technique is applied to 2 months of data collected near Point Sal, California, and captures ISW and bore propagation speed and direction information that currently cannot be measured with instruments such as moorings and synthetic aperture radar (SAR).

The problem of constructing analytical solutions describing internal gravity wave fields generated by a nonlocal source of perturbations moving on the surface of a stratified medium of finite depth is considered. For a radially symmetric model source, analytical solutions expressed in terms of eigenfunctions of the basic vertical spectral problem for internal waves are obtained in the linear approximation. Two methods of solution representation, including one based on the Mittag-Leffler theorem on expansion of a meromorphic function, are proposed. Numerically computed wave fields for various modes of wave generation are presented, which illustrate two methods of analytical wave field representation.

Vortical structures and wakes of bluff bodies in homogenous and stratified environment are common and important in ocean engineering. Based on the Boussinesq approximation, a thermocline model is proposed to deal with the variable density stratified fluid, and implemented in the commercial software Simcenter STAR-CCM+ framework. The improved delayed detached eddy simulation (IDDES) modeling method is adopted to resolve the coherent vortical structures and turbulent wakes precisely and efficiently. Four conditions consisting of one homogenous and three stratified fluid cases with different density gradient past a sphere at Reynolds number 3 700 are investigated. Results show that density stratification has a great impact on the vortical structures, the vertical motion is suppressed and internal waves will be induced and propagated, which is very different with that of homogenous situation. With the stratification strength increases, the vortical structures are gradually flattened, the asymmetry and anisotropy between vertical and horizontal motions are enhanced.

Purpose. The aim of the work is to test the bispectral wavelet analysis being applied as a tool for studying resonance interactions between the frequency components in the spectrum of internal waves (based on the example both of the model signals, the shape of which is similar to that of the solitons and boras, and the field observations data on temperature fluctuations resulted from the internal waves in the Gorlo Strait of the White Sea). Methods and Results. The paper represents a technique for detecting three-wave interactions in the internal waves’ spectrum. The method is based on the bispectral wavelet analysis. It permits to identify the interharmonic correlation and the magnitude of the quadratic phase relationship arising as a result of nonlinear interactions between the signal frequency components. In the first part of the paper, efficiency of the applied method was evaluated using the example of various artificial signals with quadratic nonlinearity in order to demonstrate the method features and advantages. In its second part, the method was used to analyze the temperature profiles obtained by scanning thermohaline sounding, in which the oscillations related to passing of the internal wave groups were recorded. It is shown that the waves with the 40 min period are generated due to quadratic nonlinearity. The auto-bicoherence function values confirm the fact that the higher harmonics are formed in the 60–120 min range as a result of the three-wave interactions. They change synchronously in time, and their amplitudes are proportional, that is typical of the initial stage of the waves’ nonlinear transformation. Absence of a periodic change in the biphase sign in the considered range indicates insignificant influence of the dispersion effects upon the short-period internal waves’ structure. Conclusions. The example of observations in the Gorlo Strait of the White Sea shows that the recorded asymmetric structure of the isotherm oscillations was formed being influenced by the three-wave interaction. Possibility of further application of the method for studying the processes of the internal waves’ nonlinear transformation and breaking is discussed.

The Lombok Strait, as one of the outlet straits, is part of the ITF route, which is directly adjacent to the Indian Ocean. There is a sill in the Lombok Strait, which is a place for internal wave generation. Leg-1 data from the Japan Agency for Marine-Earth Science and Technology in collaboration with the Agency for the Assessment and Application of Technology which is part of the Tropical Ocean Climate Study Expedition including CTD Yoyo and ADCP taken using ship vehicles R/V Kaiyo. CTD Snapshot from PUSHIDROSAL using the KRI Spica 934 vehicle part of the Opssurta Baruna Jaya 2 Expedition . Determination of seawater mass stratification with the criteria for the thermocline layer is ≥ 0.05 °C.m -1 . Four types of water masses were identified, Java Sea, mixed seawater mass (Java Sea - ITF) which occurred diapycnal mixing, North Pacific Subtropical Water (NPSW) and North Pacific Intermediate Water (NPIW). The seawater mass stratification in the Lombok Strait based on temperature, salinity and density which are seen to follow the internal tidal pattern. The average values for energy dissipation and vertical diffusivity for each layer and replication were 5.73 x 10 -7 W.Kg -1 and 3.67 x 10 -2 m 2. s -1 for CTD Yoyo and 2.25 x 10 -6 W.Kg -1 and 7.38 x 10 -2 m 2 .s -1 for CTD Snapshot . The value obtained is greater than the open ocean and straits in other studies. The high shear value confirms this in the thermocline layer. The Richardson gradient value> 0.25 is relatively constant in the thermocline layer.

An approximate analytical description of the nonstationary evolution of cylindrical nonlinear solitary waves with a complex structure is given. A modified Gardner equation with a boundary condition in the form of a “wide” soliton close to the limiting one is analyzed. The analysis shows a qualitative difference in the behavior of converging and diverging waves, as well as a difference from the quasi-stationary dynamics of cylindrical solitons.

Visualizations of reduced-order representations of stratified wakes of Reynolds number $$Re \in \{5,25,100\}\times 10^3$$ are presented at a fixed internal Froude number. The reduced-order representations are constructed by applying proper orthogonal decomposition (POD) to numerical datasets that are high-resolution, three-dimensional and time-dependent. Due to the transient nature of the flow, the dynamics to be represented are highly non-stationary, posing a challenge for the effectiveness of POD. The translational symmetry inherent in the computational configuration is utilized for the POD analysis. This technique turns out to be effective in terms of improving the convergence of energy content represented by the POD modes and enhancing the interpretability of the temporal dynamics. Individual POD modes representing distinct dynamics of various scales are visualized. In the turbulent region, visualizations of the reconstructed vertical vorticity fields suggest that the dominant length scale of flow structures decreases with the modal index. For internal wave motions, visualizations of the reconstructed vertical velocity fields show the opposite trend, as the wavelength of internal waves observed in the wake’s ambient increases with the modal index. The temporal coefficients for a given mode are observed to vary minimally between $$Re = 2.5\times 10^4$$ and $$10^5$$ , suggesting a potential asymptote of the large-scale temporal dynamics in terms of Reynolds number.

The knowledge about the distribution of small-scale turbulence in Lake Erie is limited. The present study analyzed >600 temperature microstructure casts, from multiple stations collected during the spring and summer of 1997 and 2008–09, to map the characteristic distributions of the dissipation rate of turbulent kinetic energy ( e ) and the vertical turbulent diffusivity ( K z ) in Lake Erie. The observations were classified into three groups based on depth (Group West: 25 m), with the Group Central divided into seasonally stratified and unstratified period. Group West had the highest mean e = 3.8 × 10 - 8 m 2 s - 3 , over all depths and lowest mean K z 10 - 5 m 2 s - 1 through the bottom layer. Due to the shear instability, generated by internal waves, elevated e ~ 5 × 10 - 8 m 2 s - 3 was observed in the metalimnion of the Group Central, during the seasonally stratified period, when K z was limited. The hypolimnion was calm in Group Central ( e 10 - 8 - 10 - 9 m 2 s - 3 ), except when entrainment or basin-scale seiches accelerated the flow, leading to enhanced e 10 - 7 m 2 s - 3 and K z 10 - 3 m 2 s - 1 . We extended the turbulent kinetic energy budget, in Lake Erie, to include the surface layer. Around 58% of the energy flux entering the lake dissipated in the surface layer, and the remaining 42% in the lake interior. Both lake surface area and Wedderburn numbers provided predictions on the magnitude of K z , which decreased with increasing Wedderburn numbers at a rate slower than with increasing lake number.

Vertical mixing in the ocean is an important physical process that brings deep nutrients to the upper layer. The Tokara Strait, where the Kuroshio flows out to the North Pacific from the East China Sea, is known for a mixing hotspot, but the associated vertical nutrient transport has not been well quantified yet, especially in the intermediate layer below 200 m depth. This study involved flow, turbulence, and nitrate observations to quantify the vertical turbulent nitrate flux in the Tokara Strait and discuss its impact on the Kuroshio nutrient transport. Temporal variation of current velocity, derived from a 3.5-day mooring observation, captured semi-diurnal internal waves propagating vertically at depths between 200 and 400 m. Vertical shear associated with the semi-diurnal flow was elevated at this depth range. Vertical shear due to the mean and the diurnal flow was also elevated at about 220 m and 400 m depths, respectively. Mean vertical eddy diffusivity was elevated to O(10–3–10–2 m2 s−1) at the density layers of 25.2–26.4 σθ (200–450 m depth). Associated vertical turbulent nitrate flux reached O(10 mmol m−2 day−1), especially at around 25.6 σθ (250 m depth) and 26.2–26.4 σθ (400–450 m depth). The enhanced vertical turbulent nitrate flux suggests a large amount of nitrate is injected vertically to the nutrient stream from the layer just above the North Pacific Intermediate Water and is transported throughout the core of the Kuroshio nutrient stream situated at 25.0–26.2 σθ.