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Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. We present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips’ classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.

Linear and nonlinear barotropic vorticity model frameworks are constructed to understand the formation of the monsoon trough in boreal summer over the western North Pacific. The governing equation is written with respect to specified zonal background flows, and a wave perturbation is prescribed in the eastern boundary. Whereas a uniform background mean flow leads no scale contraction, a confluent background zonal flow causes the contraction of zonal wavelength. Under linear dynamics, the wave contraction leads to the development of smaller scale vorticity perturbations. As a result, there is no upscale cascade. Under nonlinear dynamics, cyclonic (anticyclonic) wave disturbances shift northward (southward) away from the central latitude due to the vorticity segregation process. The merging of small-scale cyclonic and anticyclonic perturbations finally leads to the generation of a pair of large-scale cyclonic and anti-cyclonic vorticity gyres, straddling across the central latitude. The large-scale cyclonic circulation due to nonlinear upscale cascade can be further strengthened through a positive convection-circulation feedback.

The high-precision Juno gravitational measurements allow us to infer the structure of Jupiter's deep atmospheric zonal flow. Since this inference is nonunique, it is important to explore the space of possible solutions. In this paper, we consider a model in which Jupiter's deep atmospheric zonal flow is barotropic, or invariant along the direction of the rotation axis, until it is truncated at depth by some dynamical process (e.g., Reynolds stress, Lorentz or viscous force). We calculate the density perturbation produced by the $z$-invariant part of the flow using the thermal wind equation and compare the associated odd zonal gravitational harmonics ($J_{3}$, $J_{5}$, $J_{7}$, $J_{9}$) to the Juno-derived values. Most of the antisymmetric gravitational signal measured by Juno can be explained by extending observed winds between $20.9^{\circ}\rm{S}-26.4^{\circ}\rm{N}$ to depths of $\sim 1000$ km. Because the small-scale features of the mid/high latitude zonal flow may not persist to depth, we allow the zonal flow in this region to differ from the observed surface winds. We find that the Juno odd zonal gravitational harmonics can be fully explained by $\sim 1000$ km deep barotropic zonal flows involving the observed winds between $20.9^{\circ}\rm{S}-26.4^{\circ}$N and a few broad mid/high latitude jets., Published in JGR: Planets

We consider torsional Alfven waves which may be excited in Jupiter's metallic hydrogen region. These axisymmetric zonal flow fluctuations have previously been examined for incompressible fluids in the context of Earth's liquid iron core. Theoretical models of the deep-seated Jovian dynamo, implementing radial changes of density and electrical conductivity in the equilibrium model, have reproduced its strong, dipolar magnetic field. Analysing such models, we find anelastic torsional waves travelling perpendicular to the rotation axis in the metallic region on timescales of at least several years. Being excited by the more vigorous convection in the outer part of the dynamo region, they can propagate both inwards and outwards. When being reflected at a magnetic tangent cylinder at the transition to the molecular region, they can form standing waves. Identifying such reflections in observational data could determine the depth at which the metallic region effectively begins. Also, this may distinguish Jovian torsional waves from those in Earth's core, where observational evidence has suggested waves mainly travelling outwards from the rotation axis. These waves can transport angular momentum and possibly give rise to variations in Jupiter's rotation period of magnitude no greater than tens of milliseconds. In addition these internal disturbances could give rise to a 10% change over time in the zonal flows at a depth of 3000 km below the surface. Crown Copyright (C) 2019 Published by Elsevier B.V.

Ion- and electron-scale microinstabilities and the linear zonal-flow response in mixture plasmas with the medium-Z impurity and He-ash are investigated by means of a multi-species gyrokinetic model. In addition to the charge and dilution effects, stabilization/destabilization by nonthermal He-ash ions is clarified.

The impact of magnetic geometry on zonal-flow generation in ion temperature gradient driven turbulence is investigated by means of linear and nonlinear gyrokinetic simulations. The modulation of geodesic curvature on various configurations has revealed amplification of the zonal-flow intensity in relatively smaller geodesic curvature. Based on these findings, a nonlinear proxy model for explorations of novel magnetic geometry to activate the zonal-flow dynamics is proposed.

An analytic estimate of the lower bounds on zonal enstrophy has been studied for the beta-plane model of two-dimensional barotropic flow. The estimate provides exact lower bounds on the zonal enstrophy, which hence must be satisfied regardless of the dynamics. The energy, impulse, circulation as well as the total enstrophy are invoked as constraints for the minimization of the zonal enstrophy. The corresponding variational principle has an unusual mathematical structure (primarily because the target functional is not a coercive form), by which the constraints work out in an interesting way. A discrete set of zonal enstrophy levels is generated by the energy constraint; each level is specified by an eigenvalue that represents the meridional mode number of zonal flow. However, the value itself of the zonal enstrophy level is a function of only impulse and circulation, being independent of the energy (and total enstrophy). Instead, the energy works in selecting the ‘level’ (eigenvalue) of the relaxed state. The relaxation occurs by emitting small-scale wavy enstrophy, and continues as far as the nonlinear effect, scaled by the energy, can create wavy enstrophy. Comparison to numerical simulations shows that the theory gives a consistent estimate of the zonal enstrophy in the relaxed state.

Thermal tides, stationary waves, and general circulation are investigated using a T63 Venus general circulation model (GCM) with solar and thermal radiative transfer in the presence of high-resolution surface topography, based on time average analysis. The simulated wind and static stability are very similar to the observed ones (e.g., Horinouchi et al., 2018; Ando et al., 2020). The simulated thermal tides accelerate an equatorial superrotational flow with a speed of ~90 m s−1 around the cloud-heating maximum (~65 km). The zonal-flow acceleration rates of 0.2–0.5 m s−1 Earth day−1 are produced by both horizontal and vertical momentum fluxes at low latitudes. In the GCM simulation, strong solar heating above the cloud top (>69 km) and infrared heating around the cloud bottom (~50 km) modify the vertical structures of thermal tides and their vertical momentum fluxes, which accelerate zonal flow at 103 Pa (~75 km) and 104 Pa (~65 km) at the equator and around 103 Pa at high latitudes. Below and in the cloud layer, surface topography weakens the zonal-mean zonal flow over the Aphrodite Terra and Maxwell Montes, whereas it enhances the zonal flow in the southern polar region. The high-resolution topography produces stationary fine-scale bow structures at the cloud top and locally modifies the variances in the geographical coordinates (i.e., the activity of unsteady wave components). Over the high mountains, vertical spikes of the vertical wind variance are found, indicating penetrative plumes and gravity waves. Negative momentum flux is also locally enhanced at the cloud top over the equatorial high mountains. In the solar-fixed coordinate system, the variances (i.e., the activity of waves other than thermal tides) of flow are relatively higher on the nightside than on the dayside at the cloud top. Strong dependences of the eddy heat and momentum fluxes on local time are predominant. The local-time variation of the vertical eddy momentum flux is produced by both thermal tides and solar-related, small-scale gravity waves on the nightside., Highlights • 3D structures of stationary wave and thermal tide are examined using Venus GCM. • High-resolution topography produces fine-scale wave patterns around the cloud top. • Both equatorward and vertical momentum fluxes of thermal tide accelerate zonal flow. • Longitudinal variations of eddy momentum and heat fluxes are found at the cloud top. • Longitudinal variations of variances are caused by solar and topographic forcings.

A series of experiments with rotating, electromagnetically forced, turbulent flows were carried out at the Sapienza University of Rome to investigate the eddy–wave duality in flows with a β-effect and the electromagnetic force acting in the westward direction. When the β-effect is significant, i.e., as in planetary atmospheric and oceanic circulations, nonlinear eddy/wave interactions facilitate flow self-organization into zonal patterns in which Rossby waves and westward propagating cyclonic and anticyclonic eddies coexist. Upon time averaging, eddies disappear and the flow pattern transforms into a system of alternating zonal jets. What is the relationship between eddies, jets, and Rossby waves? To address this issue, we designed a laboratory experiment in which a westward zonal flow is produced by applying an electro-magnetic small-scale forcing to a thin layer of a rotating fluid. In order to investigate different levels of flow zonality and a wider range of zonal modes, we varied the forcing intensity and the area of the forced sector. The zonal flow evolves as a system of westward propagating, large scale, cyclonic, and anticyclonic eddies. The propagation speed of the traveling structures was calculated from the Hovmöller diagrams of both the streamfunction and the centroids of clusters of different types (cyclonic and anticyclonic eddy cores and saddle point neighborhoods) obtained via an Okubo–Weiss analysis. The results were compared with the theoretical phase speed of a Rossby wave. The correspondence between these two characteristics at the radius of maximum shear corresponding to the epicenter of the barotropic instability is quite good, particularly after including the radial variation of the zonal velocity in the β-term. It is concluded that the Rossby waves and eddies are inseparable as the former maintain the instability that sustains the latter. This symbiosis visually resembles the Rossby soliton.

In the first 20 orbits of the Juno spacecraft around Jupiter, we have identified a variety of wave‐like features in images made by its public‐outreach camera, JunoCam. Because of Juno's unprecedented and repeated proximity to Jupiter's cloud tops during its close approaches, JunoCam has detected more wave structures than any previous surveys. Most of the waves appear in long wave packets, oriented east‐west and populated by narrow wave crests. Spacing between crests were measured as small as ~30 km, shorter than any previously measured. Some waves are associated with atmospheric features, but others are not ostensibly associated with any visible cloud phenomena and thus may be generated by dynamical forcing below the visible cloud tops. Some waves also appear to be converging, and others appear to be overlapping, possibly at different atmospheric levels. Another type of wave has a series of fronts that appear to be radiating outward from the center of a cyclone. Most of these waves appear within 5° of latitude from the equator, but we have detected waves covering planetocentric latitudes between 20°S and 45°N. The great majority of the waves appear in regions associated with prograde motions of the mean zonal flow. Juno was unable to measure the velocity of wave features to diagnose the wave types due to its close and rapid flybys. However, both by our own upper limits on wave motions and by analogy with previous measurements, we expect that the waves JunoCam detected near the equator are inertia‐gravity waves., Key Points In the first 20 orbits of the Juno mission, over 150 waves and wave‐like features have been detected by the JunoCam public‐outreach cameraA wide variety of wave morphologies were detected over a wide latitude range, but the great majority were found near Jupiter's equatorBy analogy with previous studies of waves in Jupiter's atmosphere, most of the waves detected are likely to be inertia‐gravity waves

We studied the dynamics of the solar atmosphere in the region of a large quiet-Sun filament, which erupted on 21 October 2010. The filament eruption started at its northern end and disappeared from the H$\alpha$ line-core filtergrams line within a few hours. The very fast motions of the northern leg were recorded in ultraviolet light by AIA. We aim to study a wide range of available datasets describing the dynamics of the solar atmosphere for five days around the filament eruption. This interval covers three days of the filament evolution, one day before the filament growth and one day after the eruption. We search for possible triggers that lead to the eruption of the filament. The surface velocity field in the region of the filament were measured by means of time-distance helioseismology and coherent structure tracking. The apparent velocities in the higher atmosphere were estimated by tracking the features in the 30.4 nm AIA observations. To capture the evolution of the magnetic field, we extrapolated the photospheric line-of-sight magnetograms and also computed the decay index of the magnetic field. We found that photospheric velocity fields showed some peculiarities. Before the filament activation, we observed a temporal increase of the converging flows towards the filament's spine. In addition, the mean squared velocity increased temporarily before the activation and peaked just before it, followed by a steep decrease. We further see an increase in the average shear of the zonal flow component in the filament's region, followed by a steep decrease. The photospheric l.o.s. magnetic field shows a persistent increase of induction eastward from the filament spine. The decay index of the magnetic field at heights around 10 Mm shows a value larger than critical at the connecting point of the northern filament end., Comment: 11 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

This paper describes stratospheric waves in ERA5 and evaluates the contributions of different types of waves to the driving of the quasi-biennial oscillation (QBO). Because of its higher spatial resolution compared to its predecessors, ERA5 is capable of resolving a broader spectrum of waves. It is shown that the resolved waves contribute to both eastward and westward accelerations near the equator, mainly by the way of the vertical flux of zonal momentum. The eastward accelerations by the resolved waves are mainly due to Kelvin waves and small-scale gravity (SSG) waves with zonal wavelengths smaller than 2000 km, whereas the westward accelerations are forced mainly by SSG waves, with smaller contributions from inertio-gravity and mixed Rossby–gravity waves. Extratropical Rossby waves disperse upward and equatorward into the tropical region and impart a westward acceleration to the zonal flow. They appear to be responsible for at least some of the irregularities in the QBO cycle.

International audience; Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown1,2, limiting our ability to probe the structure and composition of the planet3,4. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric5 and the determination of its non-zero odd gravitational harmonics J3, J5, J7 and J9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops6. Here we report an analysis of Jupiter’s even gravitational harmonics J4, J6, J8 and J10 as observed by Juno5 and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation7. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.

著者人数: 18名, Accepted: 2017-07-25, 資料番号: SA1170060000

International audience; We address the mechanisms underlying low-frequency zonal flow generation in a turbulent system through the parametric decay of collisionless trapped particle modes and its feedback on the stabilization of the system. This model is in connection with the observation of barrier transport in reduced gyrokinetic simulations (A. Ghizzo et al., Euro. Phys. Lett. 119(1), 15003 (2017)). Here the analysis is extended with a detailed description of the resonant mechanism. A key role is also played by an initial polarisation source that allows the emergence of strong initial shear flow. The parametric decay leads to the growth of a zonal flow which differs from the standard zero frequency zonal flow usually triggered by the Reynolds stress in fluid drift-wave turbulence. The resulting zonal flow can oscillate at low frequency close to the ion precession frequency, making it sensitive to strong amplification by resonant kinetic processes. The system becomes then intermittent. These new findings, obtained from numerical experiments based on reduced semi-Lagrangian gyrokinetic simulations, shed light on the underlying physics coming from resonant wave-particle interactions for the formation of transport barriers. Numerical simulations are based on a Hamiltonian reduction technique, including magnetic curvature and interchange turbulence, where both fastest scales (cyclotron and bounce motions) are gyro-averaged.

Nonlinear interaction of magnetized Rossby waves with sheared zonal flow in the Earth's ionospheric E-layer is investigated. It is shown that in case of weak nonlinearity 2D Charney vorticity equation can be reduced to the one-dimensional modified KdV equation. (C) 2019 Elsevier B.V. All rights reserved.

In conjunction with thermo-solutal convection, the turbulence generated in planetary liquid cores may be due to the role of boundary forcing through geophysically relevant mechanisms such as precession, libration and tidal forcing (Le Bars et al. 2015). In this paper, we discuss laboratory equatorial velocity measurements and selected high-resolution numerical simulations to show the generation of developed turbulence driven by longitudinal libration or tidal forcing. In both cases, the transition to saturated turbulence is driven by an elliptical instability that excites inertial modes of the system. We find striking similarities in both the transition to bulk turbulence and the enhanced zonal flow hinting at a generic fluid response independent of the forcing mechanism. We finally discuss the relevance of this work to the planetary regime and possible directions for future investigations.

This study explores the role of inertial instability in poleward momentum surges and “flare ups” of the subpolar jet near midlatitude cyclones. Two cases are simulated with the University of Wisconsin Nonhydrostatic Modeling System to investigate the mechanisms involved in jet accelerations downstream of quasi-stationary “digging troughs.” Deep convection along the cold front leads to regions of inertial instability in the upper troposphere, which are intimately linked to jet accelerations. Terms in the zonal and meridional wind equations following the motion are evaluated for a selected air parcel within the inertially unstable region. A two-stage synoptic evolution is diagnosed, which is a characteristic signature of inertial instability. First, meridional flow accelerates following the motion, because of the subgeostrophic zonal flow and strong northward pressure gradient force (a statement of inertial instability). Second, supergeostrophic poleward flow leads to zonal acceleration and a jet flare-up. Inertial instability thus effectively displaces a westerly jet maximum poleward relative to inertially stable conditions. The structure of the poleward surge involves a distinctive “head” of high angular momentum, with the region of inertial instability enclosing the jet maximum and a core of strongly negative potential vorticity inside the surge. Departures from angular momentum–conserving profiles during meridional displacement are interpreted in terms of the pressure gradient force and degree of inertial stability. Inertial instability reduces the resulting zonal wind profile relative to angular momentum conservation but provides a significant poleward displacement of the resulting zonal wind maximum.

In the present work, we investigate the behavior of the equatorial F region zonal plasma drifts over the Peruvian region under magnetically disturbed conditions during two solar minimum epochs, one of them being the recent prolonged solar activity minimum. The study utilizes the vertical and zonal components of the plasma drifts measured by the Jicamarca (11.95°S; 76.87°W) incoherent scatter radar during two events that occurred on 10 April 1997 and 24 June 2008 and model calculation of the zonal drift in a realistic ionosphere simulated by the Sheffield University Plasmasphere-Ionosphere Model-INPE. Two main points are focused: (1) the connection between electric fields and plasma drifts under prompt penetration electric field during a disturbed periods and (2) anomalous behavior of daytime zonal drift in the absence of any magnetic storm. A perfect anticorrelation between vertical and zonal drifts was observed during the night and in the initial and growth phases of the magnetic storm. For the first time, based on a realistic low-latitude ionosphere, we will show, on a detailed quantitative basis, that this anticorrelation is driven mainly by a vertical Hall electric field induced by the primary zonal electric field in the presence of an enhanced nighttime E region ionization. It is shown that an increase in the field line-integrated Hall-to-Pedersen conductivity ratio ∑H∑P, which can arise from precipitation of energetic particles in the region of the South American Magnetic Anomaly, is capable of explaining the observed anticorrelation between the vertical and zonal plasma drifts. Evidence for the particle ionization is provided from the occurrence of anomalous sporadic E layers over the low-latitude station, Cachoeira Paulista (22.67°S; 44.9°W)—Brazil. It will also be shown that the zonal plasma drift reversal to eastward in the afternoon two hours earlier than its reference quiet time pattern is possibly caused by weakening of the zonal wind system during the prolonged solar minimum period.

Meteor radar data collected over Langfang, China (39.4&deg, N, 116.7&deg, E) were used to estimate the momentum flux of short-period (less than 2 h) gravity waves (GWs) in the mesosphere and lower thermosphere (MLT), using the Hocking (2005) analysis technique. Seasonal variations in GW momentum flux exhibited annual oscillation (AO), semiannual oscillation (SAO), and quasi-4-month oscillation. Quantitative estimations of GW forcing toward the mean zonal flow were provided using the determined GW momentum flux. The mean flow acceleration estimated from the divergence of this flux was compared with the observed acceleration of zonal winds displaying SAO and quasi-4-month oscillations. These comparisons were used to analyze the contribution of zonal momentum fluxes of SAO and quasi-4-month oscillations to zonal winds. The estimated acceleration from high-frequency GWs was in the same direction as the observed acceleration of zonal winds for quasi-4-month oscillation winds, with GWs contributing more than 69%. The estimated acceleration due to Coriolis forces to the zonal wind was studied, the findings were opposite to the estimated acceleration of high-frequency GWs for quasi-4-month oscillation winds. The significance of this study lies in estimating and quantifying the contribution of the GW momentum fluxes to zonal winds with quasi-4-month periods over mid-latitude regions for the first time.

The dynamics of solar tachocline is of importance in the solar magnetic activity; the underlying physics of tachocline dynamics, however, remains unclear. Studies of tachocline have shown that the nonlinear interaction of Rossby waves— a process of inhomogeneous mixing of potential vorticity (PV)— forms a zonal jet, while a mean toroidal magnetic field (B-field) suppresses the zonal flow with a critical parameter proportional to B2/η, where η is the magnetic diffusivity (Tobias et al. 2007). Thus, the role of toroidal B-field is of significance in turbulence properties of the tachocline. As a simple model of an incompressible and stably stratified tachocline, we consider a rotating, two-dimensional model— β-plane— and examine the effect of a mean B-field on the PV mixing in the β-plane turbulence. We report an analytical theory of jet suppression due to the mean B-field, which also enters as a modification of the cross phase in the vorticity flux, and as an initiator for a flow along the tiled field lines. A mean field equation for the vorticity and comparisons of real-space and k-space formulations will also be presented by using closure and quasi-linear approximations. *This work is supported by the U.S. Department of Energy under Award No. DE-FG02-04ER54738.

The influence of the recent deep and prolonged solar minimum on the daytime zonal and vertical plasma drift velocities during quiet time is investigated in this work. Analyzing the data obtained from incoherent scatter radar from Jicamarca (11.95° S, 76.87° W) we observe an anomalous behavior of the zonal plasma drift during June 2008 characterized by lower than usual daytime westward drift and its early afternoon reversal to eastward. As a case study the zonal drift observed on 24 June 2008 is modeled using a realistic low-latitude ionosphere simulated by the Sheffield University Plasmasphere-Ionosphere Model-INPE (SUPIM-INPE). The results show that an anomalously low zonal wind was mainly responsible for the observed anomalous behavior in the zonal drift. A comparative study of the vertical plasma drifts obtained from magnetometer data for some periods of maximum (2000–2002) and minimum solar activity (1998, 2008, 2010) phases reveal a considerable decrease on the E-region conductivity and the dynamo electric field during 2008. However, we believe that the contribution of these characteristics to the unusual behavior of the zonal plasma drift is significantly smaller than that arising from the anomalously low zonal wind. The SUPIM-INPE result of the critical frequency of the F layer (foF2) over Jicamarca suggested a lower radiation flux than that predicted by solar irradiance model (SOLAR2000) for June 2008.

The dipole structure of the North Atlantic Oscillation (NAO) is examined in this study by defining the tilt of the NAO dipole centers on synoptic time scales. All the positive NAO phase (NAO+) and negative NAO phase (NAO&minus, ) events are divided into three tilting types according to their definition, namely, northeast&ndash, southwest (NE&ndash, SW), north&ndash, south symmetric (N&ndash, S, not tilted), and northwest&ndash, southeast (NW&ndash, SE) tilting NAO events. Then, the associated surface air temperature (SAT), geopotential height, zonal wind, and SST (surface sea temperature) anomalies of each type are examined. It is found that, for different asymmetric NAO tilt types, the local SATs exhibit significantly different distributions. The zonal wind has a good match with the NAO dipole tilt, which also includes the positive feedback of the NAO circulation. The basic zonal flow that removes the NAO days also exhibits a clear tilt structure that favors the tilt of the NAO dipole. Moreover, it is found that the Atlantic Multidecadal Oscillation (AMO) may be an important factor affecting the tilt of the NAO dipole. The AMO index has a significant 15-year lead for the NAO index and basic zonal flow index, with a high correlation coefficient, which might be seen as a precondition that indicates the tilt of the NAO events, especially on decadal or multidecadal time scales. However, the physical mechanisms and processes are still not fully understood.

The pattern of migrating zonal flow bands associated with the solar cycle, known as the torsional oscillation, has been monitored with continuous global helioseismic observations by the Global Oscillations Network Group, together with those made by the Michelson Doppler Imager onboard the Solar and Heliosepheric Observatory and its successor the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, since 1995, giving us nearly two full solar cycles of observations. We report that the flows now show traces of the mid-latitude acceleration that is expected to become the main equatorward-moving branch of the zonal flow pattern for Cycle 25. Based on the current position of this branch, we speculate that the onset of widespread activity for Cycle 25 is unlikely to be earlier than the middle of 2019., Comment: 8 pages, 5 figures, accepted by ApJL 5 July 2018

An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring., P. Z.-G. acknowledges financial support by Grant CGL2015-72259-EXP by the Ministry of Economy and Competitivity of Spain. This work has been partly done during P. Z.-G.’s visit to Princeton, funded by NSF Grant AGS-1733818.

Solar torsional oscillations are migrating bands of slower- and faster-than-average rotation, which are strongly related to the Sun's magnetic cycle. We perform a long-term study (16 yr) of hemispherical asymmetry in solar torsional oscillation velocity using helioseismic data for the first time. We study the north-south asymmetry in the velocity using the zonal flow velocities obtained by ring diagram analysis of the Global Oscillation Network Group (GONG) Doppler images. We find significant hemispherical asymmetry in the torsional oscillation velocity and explore its variation with respect to depth, time, and latitude. We also calculate the hemispherical asymmetry in the surface velocity measurements from the Mount Wilson Observatory and the zonal flow velocities obtained from the Helioseismic and Magnetic Imager ring diagram pipeline. These asymmetries are found to be consistent with the asymmetry obtained from GONG observations. We show that the asymmetry in near-surface torsional oscillation velocity is correlated with the asymmetry in magnetic flux and sunspot number at the solar surface, with the velocity asymmetry preceding the flux and sunspot number asymmetries. We speculate that the asymmetry in torsional oscillation velocity may help in predicting the hemispherical asymmetry in sunspot cycles., Comment: Accepted for publication in The Astrophysical Journal

The westward drift component of the secular variation is likely to be a signal of waves riding on a background mean flow. By separating the wave and mean flow contributions, we can infer the strength of the “hidden” azimuthal part of the magnetic field within the core. We explore the origin of the westward drift commonly seen in dynamo simulations and show that it propagates at the speed of the slow magnetic Rossby waves with respect to a mean zonal flow. Our results indicate that such waves could be excited in the Earth's core and that wave propagation may indeed play some role in the longitudinal drift, particularly at higher latitudes where the wave component is relatively strong, the equatorial westward drift being dominated by the mean flow. We discuss a potential inference of the RMS toroidal field strength within the Earth's core from the observed drift rate.

The Venus Monitoring Camera (VMC) acquired a set of ultraviolet (UV) images during the Venus Express mission unprecedented in its duration from May 2006 to September 2013. Here we present the results of digital tracking of the cloud features in the upper cloud layer at latitudes 25–75°S using images from 257 orbits with the best spatial coverage. The method relies on analysis of correlations between pairs of UV images separated in time. The bulk of data processed allows us to clarify the reasons why the mid-latitude jet is not always present in latitudinal wind profiles. Comparing VMC images with wind velocity fields we found a relationship between cloud morphology at middle latitudes and the circulation. The vector field in middle latitudes depends on the presence of a contrast global streak in the cloud morphology tilted with respect to latitude circles. The angle of the flow deflection (the angle between the wind velocity and latitudinal circles) and the difference of the zonal velocity on the opposite sides of the streak are in direct relationship to the angle between the streak and latitude circles. During such orbits the jet bulge does not appear in the latitudinal profile of the zonal wind component. Otherwise a zonal flow with small changes of the meridional velocity dominates in middle latitudes and manifests itself as a jet bulge. The relationship between the cloud cover morphology and circulation peculiarities can be attributed to the motion of global cloud features, like the Y-feature. We prepared plots of zonal and meridional velocities averaged with respect to the entire observation period. The average zonal velocity has a diurnal maximum at 15:00 local solar time and at 40°S. The meridional velocity reaches its maximum between 13:00 and 16:00 and at 50°S. The velocities obtained by the digital method are in good agreement with results of the visual method in the middle latitudes published earlier by Khatuntsev et al. (2013) .

A wake due to islands in background zonal flow has been observed in the equatorial Pacific Ocean. This study detects and examines a wake due to the Maldives in the eastward Wyrtki jet in the Indian Ocean. Observations by acoustic Doppler current profilers deployed east of the Maldives show semiannual variability in cross-equatorial currents, which cannot be explained by annual monsoonal wind forcing. Output from a high-resolution ocean general circulation model (OGCM) shows that the semiannual current variability is a part of a stationary wavelike pattern of meridional currents, which appears east of the Maldives concurrently with the eastward Wyrtki jet. Idealized numerical experiments are conducted using a 1.5-layer model, in which an equatorial jet driven by wind forcing or steady inflow impinges islands that are similar to the Maldives in shape. The results show the meandering of the equatorial eastward jet east of the model islands, and the resulting cross-equatorial currents have a similar pattern compared to those in the OGCM simulation. The momentum budget analysis obtained from the OGCM simulation and the layer model experiments shows a significant contribution of momentum advection to the generation of the wake. Also, the layer model experiments exhibit that the wake is essentially stationary; its zonal wavelength becomes larger when the eastward jet is stronger, and the wake is absent when the equatorial jet is westward. The similarity of the wake in the equatorial jet to stationary damped Rossby waves in the quasigeostrophic barotropic ocean model is discussed.

Tropical waves are generally considered to have a baroclinic structure. However, analysis of ERA-Interim and NOAA OLR data for the period 1979–2010 shows that in the equatorial and Northern Hemisphere near-equatorial regions in the tropical Western Hemisphere (WH), westward- and eastward-moving transients, with zonal wavenumbers 2–10 and periods of 2–30 days, have little tilt in the vertical and can be said to be equivalent barotropic. The westward-moving transients in the equatorial region have large projections onto the westward mixed Rossby–gravity (WMRG) wave and those in the near-equatorial region project onto the gravest Rossby wave and also the WMRG. The eastward-moving transients have large projections onto the Doppler-shifted eastward-moving versions of these waves. To examine how such equivalent barotropic structures are possible in the tropics, terms in the vorticity equation are analyzed. It is deduced that waves must have westward intrinsic phase speeds and can exist in the WH with its large westerly vertical shear. Throughout the depth, the advection of vorticity by the zonal flow and the β term are large and nearly cancel. In the upper troposphere the zonal advection by the strong westerly flow wins and the residual is partially balanced by vortex shrinking associated with divergence above a region of ascent. Below the region of ascent the β term wins and is partially balanced by vortex stretching associated with the convergence. An equivalent barotropic structure is therefore maintained in a similar manner to higher latitudes. The regions of ascent are usually associated with deep convection and, consistently, WH waves directly connected to tropical convection are also found to be equivalent barotropic.

Observational data are used to test the hypothesis that the basic state modulates the dispersion properties of convectively coupled equatorial waves (CCEWs). This hypothesis is based on shallow water theory, which predicts that the zonal speed of propagation of such tropospheric equatorial modes is altered by the equivalent depth and the basic zonal flow. Localized space-time spectra are calculated to investigate how CCEW spectral peaks vary across the tropics and how they are affected by the variations in zonal wind observed geographically and by season. Doppler shifting by the basic state barotropic zonal flow is readily identified. Once this Doppler shifting is taken into account, the equivalent depths of CCEWs inferred from global power spectra are surprisingly uniform, both geographically and temporally. However, there are also detectable modulations that appear consistent with changes in vertical shear of the zonal flow, along with other shifts that are not as easily explained.

Baroclinic instability in the super-rotation of Venus is investigated by a newly developed atmospheric general circulation model. First, we adopt an idealized super-rotation, i.e., solid-body rotating flow in a weakly stratified layer at cloud level, as an initial basic state in a nominal case. With the evolution of time, baroclinic instability occurs in a weakly stratified layer with large vertical shear of the basic zonal flow. Horizontal wind associated with the baroclinic instability modes is of a few m s−1. The initial structure of the unstable modes is similar to those obtained in previous linear stability analyses. However, it is modified by nonlinear interactions in the later stage, reaching a quasi-steady state. Meridional transport of momentum and heat by these unstable modes accelerates the super-rotation by ~ 0.05 m s−1 day−1 at midlatitudes. Furthermore, the dependence of baroclinic instability on the basic state, i.e., the meridional profiles of zonal flow and the vertical profiles of static stability, are subsequently investigated. For the super-rotation with midlatitude jets at cloud level, the modes are modified from baroclinic to barotropic in the later stage. Typically, their horizontal wind is of O(10) m s−1. Their amplitude is maintained by energy conversion from zonal-mean available potential energy associated with the baroclinic basic state. In the case where static stability is smaller than that in the nominal case, the baroclinic modes transfer angular momentum from midlatitude to the equator near a 70 km level and accelerate the super-rotation by more than 10 m s−1 in the equatorial region.

This study examines the zonal momentum budget along the equator in the Indian Ocean in a high-resolution ocean general circulation model. Wyrtki Jets, wind-driven eastward flows in the upper 100 m that appear typically twice per year in boreal spring and fall, are a prominent feature of the ocean circulation in this region. Our results indicate that nonlinearity associated with these jets is an important element of the zonal momentum budget, with wind driven eastward momentum advected downward into the thermocline. This advection results in annually averaged zonal currents that flow against the zonal pressure gradient in the upper 200 m, such that there is no mean subsurface undercurrent in the Indian Ocean as there is in the Pacific and Atlantic Oceans. Zonal momentum is further distributed along the equator by zonal advection, with eastward flow substantially enhanced in the eastern basin relative to the western basin. Meridional advection, though generally weak, tends to decelerate surface eastward flow along the equator. These results contrast with those from previous idealized wind-forced model experiments that primarily emphasized the importance of vertical momentum advection. Also, beyond semiannual period fluctuations, significant momentum advection results from a broad range of interacting processes, spanning intraseasonal to interannual time scales. We conclude that proper simulation of zonal flows along the equator in the Indian Ocean, including their climatically relevant impacts on the mass and heat balance, requires accurate representation of nonlinearities that derive from a broad range of time and space scales.

Solar torsional oscillations are migrating bands of slower and faster than average rotation, which are thought to be related to the Sun’s magnetic cycle. We perform the first long-term study (16 years) of hemispherical asymmetry in solar torsional oscillation velocity using helioseismic data. We explore the spatial and temporal variation of North-South asymmetry using zonal flow velocities obtained from ring diagram analysis of the Global Oscillation Network Group (GONG) Doppler images. We find a strong correlation between the asymmetries of near-surface torsional oscillation with magnetic flux and sunspot number, with the velocity asymmetry preceding in both the cases. We speculate that the asymmetry in torsional oscillation velocity may help in predicting the hemispherical asymmetry in the sunspot cycle.

We perform a computational study of characteristics of coupled drift wave (DW)-parallel velocity gradient (PVG) driven turbulence. The three-dimensional Hasegawa–Mima equation combined with ion parallel flow dynamics is used for this study. Energetic analyses, both analytic and computational, show the energy equipartition of the parallel Reynolds power (i.e. the free energy due to a gradient in equilibrium parallel velocity) in parallel and perpendicular directions. A considerable portion of the perpendicular energy that is transferred through the parallel coupling generates the perpendicular zonal flow (ZF), implying the increase of the ZF level when an equilibrium PVG is present. A careful analysis of parallel-perpendicular coupling dynamics shows that the vortex stretching-like term in this system plays a significant role in the ZF generation. This is in contrast to the neutral fluid turbulence where it hinders the inverse cascade process. However, the ZF generation from PVG turbulence is found to be less effective in comparison with that of DW turbulence.

From global gyrokinetic simulations of toroidal ion temperature gradient-driven turbulence, we show that the ion parallel compression has a strong influence on the generation and radial profile formation of zonal flows. The kinetic potential vorticity (PV) flux and its fluid expression are used to elucidate the zonal flow generation mechanism. In the absence of sheared equilibrium flow, the dominant contributions to the net PV flux are shown to come from the parallel compression and the grad-B drift, and to largely cancel out each other. With a finite parallel rotation shear, however, the parallel compression-driven flux becomes dominant over the grad-B drift-driven one, leading to a change in the radial zonal flow profile. The imbalance between the parallel compression and the grad-B drifts results in a considerable amplification of the zonal flow and a reduction of turbulence fluctuation levels as compared to the non-rotating plasma. These findings demonstrate an essential role of the parallel compression in the zonal flow generation and confinement improvement for rotating tokamak plasmas.

The mechanisms of the atmospheric response to climate forcing are analyzed using an example of uniform SST warming in an idealized aquaplanet model. A 200-member ensemble of experiments is conducted with an instantaneous uniform SST warming. The zonal mean circulation changes display a rapid poleward shift in the midlatitude eddy-driven westerlies and the edge of the Hadley cell circulation and a slow equatorward contraction of the circulation in the deep tropics. The shift of the poleward edge of the Hadley cell is predominantly controlled by the eddy momentum flux. It also shifts the eddy-driven westerlies against the surface friction, at a rate much faster than the expectation from the natural variability of the eddy-driven jet (i.e., the e-folding time scale of the annular mode), with much less feedback between the eddies and zonal flow. The transient eddy–zonal flow interactions are delineated using a newly developed finite-amplitude wave activity diagnostic of Nakamura. Applying it to the transient ensemble response to uniform SST warming reveals that the eddy-driven westerlies are shifted poleward by permitting more upward wave propagation in the middle and upper troposphere rather than reducing the lower-tropospheric baroclinicity. The increased upward wave propagation is attributed to a reduction in eddy dissipation of wave activity as a result of a weaker meridional potential vorticity (PV) gradient. The reduction allows more waves to propagate away from the latitudes of baroclinic generation, which, in turn, leads to more poleward momentum flux and a poleward shift of eddy-driven winds and Hadley cell edge.

An analytical model, previously developed for investigating the propagation of equatorially-trapped waves on an equatorial beta-plane in a uniform zonal flow in the presence of Rayleigh friction and Newtonian cooling in the Earth's stratosphere, is applied to Jupiter's upper troposphere and lower stratosphere. By analogy with the Earth, a 'spectral window' is identified for each of the main classes of equatorial wave mode, suggesting a mode-selection criterion for the dominant modes observed in association with strong wave-zonal flow interactions in the stratosphere. The modes favoured by this approach are compared with recent observations of wave activity and the quasi-quadrennial oscillation (QQO) in Jupiter's tropical atmosphere. Two modes with zonal wavenumber k similar to 8-11 are identified which may correspond to: (i) an equatorial Rossby mode moving eastward at around 100 m s(-1): and (ii) a mixed Rossby-gravity mode which is similar to stationary in System III, apparently excited by a wave source moving with the zonal wind in the deep troposphere. A Kelvin mode is also predicted to be present, but observational evidence for this mode is lacking to date. A numerical model, capable of solving for wave structures and wave-zonal flow interactions in arbitrary zonal flows using a Hermite spectral method, is adapted to conditions in Jupiter's stratosphere. The latter numerical model is shown to successfully simulate a plausible QQO with a period around four Earth years, given a single pair of forced Kelvin and MRG modes with tropospheric amplitudes consistent with observations. This model demonstrates that the QQO may indeed result, at least in principle, from interactions of a small number of equatorially-trapped wave modes with the zonal flow in the stratosphere. The selection of wave modes taking part in this process is not unique, however, and the precise identification of the relevant modes from observations remains elusive. (C) 2000 Elsevier Science Ltd. All rights reserved.

The nature of the flow below the cloud level on Jupiter and Saturn is still unknown. Relating the flow on these planets to perturbations in their density field is key to the analysis of the gravity measurements expected from both the Juno (Jupiter) and Cassini (Saturn) spacecrafts during 2016-17. Both missions will provide latitude-dependent gravity fields, which in principle could be inverted to calculate the vertical structure of the observed cloud-level zonal flow on these planets. Theories to date connecting the gravity field and the flow structure have been limited to potential theories under a barotropic assumption, or estimates based on thermal wind balance that allow analyzing baroclinic wind structures, but have made simplifying assumptions. Those include the effects of the deviations from spherical symmetry, the centrifugal force due to density perturbations, and self-gravitational effects of the density perturbations. Recent studies attempted to include some effects but not in a self-consistent manner. The present study introduces such a self-consistent perturbation approach to the thermal wind balance that incorporates all physical effects, and applies it to several example wind structures, both barotropic and baroclinic. The contribution of each term is analyzed, and the results are compared in the barotropic limit to those of potential theory. It is found that the dominant balance involves the original simplified thermal wind approach. This balance produces a good order-of-magnitude estimate of the gravitational moments, and is able, therefore, to address the order one question of how deep the flows are given measurements of gravitational moments. The additional terms are significantly smaller and none of these terms is dominant, so any approximation attempting to improve over the simplified thermal wind approach needs to include all other terms., Journal of Fluid Mechanics - in revision - August 2016

The classic solution of Fofonoff to the problem of free inertial flow in a closed basin is extended to the case where the potential vorticity, q, is linearly proportional to the streamfunction, with a negative definite constant, − K 2 . Such a relation arises naturally in the presence of an eastward flow, instead of Fofonoff’s westward zonal flow on the β plane. The resulting solutions can be wavelike if K 2 = β L 2 / U π 2 exceeds the critical value of 1 where U is the magnitude of the eastward flow and L is the characteristic meridional scale of the motion. Solutions are presented with various boundary conditions on the basin boundaries, and conditions for which the solutions suffer a resonance are also obtained. It is suggested that oceanic circulations with eastward flows naturally excite these Fofonoff negative modes. The possibility of resonance and instability adds additional physical complexity to the modes.

Nonlinear excitation of low frequency zonal structure (LFZS) by beta-induced Alfven eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic zonal flow (ZF), rather than zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the zonal electric field has an even mode structure at the rational surface where radial envelope peaks., Comment: to be submitted to Nuclear Fusion

International audience; The turbulence generated in the liquid metal cores and subsurface oceans of planetary bodies may be due to the role of mechanical forcing through precession/nutation, libration, tidal forcing and collisions. Here, we model the response of an enclosed constant density fluid to tidal forcing by combining laboratory equatorial velocity measurements with selected high-resolution numerical simulations to show, for the first time, the generation of bulk filling turbulence. The transition to saturated turbulence is characterized by an elliptical instability that first excites primary inertial modes of the system, then secondary inertial modes forced by the primary inertial modes, and then bulk filling turbulence. The amplitude of this saturated turbulence scales with the body's elliptical distortion, U ∼ β, while a time- and radially averaged azimuthal zonal flow scales with β2. The results of the current tidal experiments are compared with recent studies of the libration-driven turbulent flows studied by Grannan et al. and Favier et al. Tides and libration correspond to two end-member types of geophysical mechanical forcings. For satellites dominated by tidal forcing, the ellipsoidal boundary enclosing the internal fluid layers is elastically deformed while, for librational forcing, the core-mantle boundary possesses an inherently rigid, frozen-in ellipsoidal shape. We find striking similarities between tidally and librationally driven flow transitions to bulk turbulence and zonal flows. This suggests a generic fluid response independent of the style of mechanical forcing. Since β ≲ 10−4 in planetary bodies, it is often argued that mechanically driven zonal velocities will be small. In contrast, our linear scaling for mechanically driven bulk turbulence, U ∼ β, suggests geophysically significant velocities that can play a significant role in planetary processes including tidal dissipation and magnetic field generation.

The purpose of this study is to investigate the effect of geomagnetic activity (used as a measure of solar wind parameters) on the variability of large-scale climate patterns and on changes in the global temperature. We show that positive statistically significant correlations between global temperature and the distribution of surface temperature over Eurasia, the East and Equatorial Pacific and over the North Atlantic for the period 1966–2009 correspond to large-scale climate patterns defined by climate indices. We found very similar positive correlations between geomagnetic activity and the distribution of surface temperature in the mentioned regions. As an effect of geomagnetic storms, energetic particles penetrate from the magnetosphere into the region of the stratospheric polar vortex. The increase of temperature and pressure can be observed over northern Canada. The vortex shifts towards Europe, rotates counter-clockwise and the wind blows from the polar region over Greenland southwards. It diverts the warm flow proceeding northward over the Atlantic, eastward along the deep Icelandic low extending as far as the Barents Sea and takes part in warming Eurasia. The strengthened zonal flow from Siberia cools the western Pacific with the impact on the warming of the equatorial and eastern Pacific when also a distinct 1976–78 climate shift occurred. Processes in the Atlantic and Pacific play a significant role and a time delay (wind forcing over the previous 1–4 yr) appears to be the most important for the relocation of the oceanic gyres. Results showing statistically significant relations between time series for geomagnetic activity, for the sum of climate indices and for the global temperature help to verify findings concerning the chain of processes from the magnetosphere to the troposphere.

Two important dynamical processes influence the extratropical zonal wind field: angular momentum transport by the thermally direct Hadley circulation (thermal-driving T) and momentum flux convergence by atmospheric waves (eddies) that develop in regions of enhanced baroclinicity (eddy-driving E). The relationship between extratropical zonal wind variability and these driving processes is investigated using 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) data. Indices representing the processes (iT and iE) are defined based on vertically integrated diabatic heating and meridional convergence of the meridional flux of zonal momentum by eddies, respectively. Zonal wind signatures associated with these indices are identified via composite analysis. In the Atlantic sector, zonal wind variability is mainly associated with momentum flux convergence by baroclinic eddies, supporting the established view that the Atlantic jet is primarily eddy driven. In the Pacific sector, zonal wind variability is associated with both driving processes, evidence that the Pacific jet is both thermally driven and eddy driven. The thermally driven Pacific signature reflects changes in jet strength (intensity and longitudinal extent) with some resemblance to the zonal wind anomalies of the Pacific–North America (PNA) pattern. The eddy-driven signature reflects a latitudinal shift of the jet exit region in both sectors that resembles the zonal wind anomalies of the North Atlantic Oscillation (NAO) or West Pacific (WP) patterns.

A thin layer of an ideal gas on a solid gravitating sphere is considered with allowance for inertia forces. Flows are initiated by heating the solid spherical surface nonuniformly in latitudes. A solution in the form of a one-dimensional flow directed along the meridians is obtained. Assuming that the gas density is independent of the latitude, an exact solution is obtained for the one-dimensional flow in question. This solution has all the features of zonal winds existing in many planets of the Sun system including the possibility of existence of supperrotation, i.e., the regime for which the atmosphere moves more rapidly than the solid body of the planet.

The large-scale dynamics of the solar convection zone have been inferred using both global and local helioseismology applied to data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) on board SOHO. The global analysis has revealed temporal variations of the “torsional oscillation” zonal flow as a function of depth, which may be related to the properties of the solar cycle. The horizontal flow field as a function of heliographic position and depth can be derived from ring diagrams, and shows near-surface meridional flows that change over the activity cycle. Time-distance techniques can be used to infer the deep meridional flow, which is important for flux-transport dynamo models. Temporal variations of the vorticity can be used to investigate the production of flare activity. This paper summarizes the state of our knowledge in these areas.

The emerging understanding of instability-driven plasma-turbulence saturation in terms of energy transfer to stable modes in the same scale range as the instability is employed to derive a saturation theory for the toroidal branch of ion temperature gradient turbulence that provides the scaling of turbulence and zonal flow levels for all physical parameters. The theory is based on the eigenmode decomposition of a nonlinear fluid model, which is subjected to a statistical closure and simplified via an ordering expansion consistent with zonal-flow catalyzed energy transfer from the unstable mode to the stable mode at large scale. Solution of the closed energy balance equations yields a turbulence level that is proportional to the ratio of the zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio of the growth rate and the inverse triplet correlation time. The saturation scalings a...

Analytical theory is used to examine the linear response of a meridionally unbounded stratified ocean to large-scale, low-frequency wind forcing. The following results, applied mainly to the equatorial Pacific, were obtained. (i) Provided that the wind stress curl vanishes at large distance from the equator, a general Sverdrup solution is valid in the quasi-steady (frequency ω → 0) limit. The meridionally averaged zonal flow toward the western boundary layer is zero so that there is no net mass flow into the boundary layer and the large-scale boundary condition is therefore satisfied. This solution predicts a zero pycnocline response in the eastern equatorial Pacific. It therefore predicts that, for the eastern equatorial Pacific, a slow weakening of the equatorial trade winds will not lead to long-term El Niño conditions there. (ii) Consistent with observations and other previous work, for finite but small frequencies there are two modes of equatorial motion. One is a “tilt” mode in which the equatorial sea level and thermocline are tilted by the in-phase zonal wind stress and the other is an equatorial warm water volume (WWV) mode in which the discharge of equatorial warm water (negative WWV anomaly) lags the wind stress forcing by a quarter of a period. (iii) The amplitude of the WWV mode approaches zero like ω1/2. Therefore, as ω → 0, the equatorial solution reduces to the tilt mode. (iv) The WWV mode is not due to a dominant meridional divergence driven by the wind, as suggested by some previous work. Meridional and zonal divergence approximately cancel. Reflection of energy at both ocean boundaries together with the strong dependence of long Rossby wave speed on latitude is crucial to the existence of the disequilibrium WWV mode. Because higher-latitude Rossby waves travel so much more slowly, the Rossby waves reflecting from the western ocean boundary are not in phase. This gives rise to a reflected equatorial Kelvin wave and a WWV that is not in phase with the wind stress forcing. (v) Observations from past work have shown that much low-frequency wave energy, particularly westward propagating Rossby wave energy poleward of about 5°N and 5°S, is damped out before it reaches the western ocean boundary. In this way dissipation likely has a strong influence on the equatorial Kelvin wave reflection and hence the disequilibrium WWV.

An idealized atmospheric model is employed to quantify the strength of the eddy feedback and the persistence of the zonal index. The strength of the surface frictional damping on the zonal index is varied, and an external zonal momentum forcing is included to compensate for the momentum change associated with the friction change such that the climatological jet latitude and shape are unchanged. The model can generate a nearly identical climatology and leading mode of the zonal mean zonal wind for different frictional damping rates, except when the jet undergoes a regime transition. For those experiments without a regime transition, as the surface friction is increased, the strength of eddy feedback is enhanced but the zonal index becomes less persistent. A simple feedback model suggests that the e-folding decorrelation time scale of the zonal index can be determined by the frictional damping rate and the strength of eddy feedback. The strength of eddy feedback is found to be related to the instantaneous vertical wind shears near the surface controlled by the frictional damping. Furthermore, the climate response to an external zonal torque is proportional to the decorrelation time scale, although the simple prediction used here overestimates the climate response by a factor of 2.

Coherent jets, such as the Jovian banded winds, are a prominent feature of rotating turbulence. Shallow-water turbulence models capture the essential mechanism of jet formation, which is systematic eddy momentum flux directed up the mean velocity gradient. Understanding how this systematic eddy flux convergence is maintained and how the mean zonal flow and the eddy field mutually adjust to produce the observed jet structure constitutes a fundamental theoretical problem. In this work a shallow-water equatorial beta-plane model implementation of stochastic structural stability theory (SSST) is used to study the mechanism of zonal jet formation. In SSST a stochastic model for the ensemble-mean turbulent eddy fluxes is coupled with an equation for the mean jet dynamics to produce a nonlinear model of the mutual adjustment between the field of turbulent eddies and the zonal jets. In weak turbulence, and for parameters appropriate to Jupiter, both prograde and retrograde equatorial jets are found to be stable solutions of the SSST system, but only the prograde equatorial jet remains stable in strong turbulence. In addition to the equatorial jet, multiple midlatitude zonal jets are also maintained in these stable SSST equilibria. These midlatitude jets have structure and spacing in agreement with observed zonal jets and exhibit the observed robust reversals in sign of both absolute and potential vorticity gradient.