# Richard C. SchoppInstitut Français de Recherche pour l'Exploitation de la Mer CNRS LPO · laboratoire de physique des océans

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The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

Nearly all the subsurface eddies detected in seismic imaging of sections in the northeast Atlantic have been assumed to be anticyclones containing Mediterranean Water (MW). Fewer MW cyclones have been observed and studied. In this study, the work of previous numerical studies is extended to investigate some characteristics of layering surrounding MW cyclones, using a primitive equation model with equal diffusivities for salinity and temperature to suppress the effects of double diffusion. It is shown that, after a stable state is reached, both anticyclones and cyclones display similar patterns of layering: stacked thin layers of high acoustic reflectivity located above and below the core of each vortex, which do not match isopycnals. The authors conclude that it should not be possible to distinguish between MW cyclones and anticyclones based on their signature in seismic imaging alone. Complementary information is needed to determine the sense of rotation.

Nearly all the sub-surface eddies detected in seismic imaging of sections in the North
East Atlantic have been assumed to be anticyclones containing Mediterranean Water
(MW). Fewer MW cyclones have been observed and studied. In this study we extend
the work of previous numerical studies to investigate some characteristics of layering
surrounding MW cyclones, using a Primitive Equations model with equal diffusivities for
salinity and temperature to suppress the effects of double-diffusion.
We show that, after a stable state is reached, both anticyclones and cyclones display
similar patterns of layering: stacked thin layers of high acoustic reflectivity located
above and below the core of each vortex which do not match isopycnals. We conclude
that it should not be possible to distinguish between MW cyclones and anticyclones
based on their signature in seismic imaging alone. Complementary information is
needed to determine the sense of rotation.

The dynamics of layering surrounding meddy-like vortex lenses is investigated from a tracer stirring point of view using a tracer advection model as well as Primitive Equation (PE) and Quasi Geostrophic (QG) models. Recent in situ data inside a meddy as well as high resolution PE simulations reveal the formation of highly density-compensated layers in temperature and salinity at the periphery of the vortex core, suggesting a predominant role of stirring in the layering process. Passive tracer experiments using a tangent-linear QG model confirm this essential aspect and show in more details the transformation of horizontal variability into vertically stacked layers. The time evolution of this process is quantified and a simple scaling is proposed and shown to describe precisely the thinning down of the layers as a function of the initial tracer column's horizontal width and the vertical shear of the azimuthal velocity. Non-linear QG simulations are performed and analysed for comparison with the work of Hua et al., (2013). A step-by-step interpretation of these results on the evolution of layering is proposed in the context of tracer stirring.

Evidence of persistent layering, with a vertical stacking of sharp variations in temperature, has been presented recently at the vertical and lateral periphery of energetic oceanic vortices through seismic imaging of the water column. The stacking has vertical scales ranging from a few metres up to 100 m and a lateral spatial coherence of several tens of kilometres comparable with the vortex horizontal size. Inside this layering, in situ data display a \$[{ k}_{h}^{- 5/ 3} { k}_{h}^{- 2} ] \$ scaling law of horizontal scales for two different quantities, temperature and a proxy for its vertical derivative, but for two different ranges of wavelengths, between 5 and 50 km for temperature and between 500 m and 5 km for its vertical gradient. In this study, we explore the dynamics underlying the layering formation mechanism, through the slow dynamics captured by quasi-geostrophic equations. Three-dimensional high-resolution numerical simulations of the destabilization of a lens-shaped vortex confirm that the vertical stacking of sharp jumps in density at its periphery is the three-dimensional analogue of the preferential wind-up of potential vorticity near a critical radius, a phenomenon which has been documented for barotropic vortices. For a small-Burger (flat) lens vortex, baroclinic instability ensures a sustained growth rate of sharp jumps in temperature near the critical levels of the leading unstable modes. Such results can be obtained for a background stratification which is due to temperature only and does not require the existence of salt anomalies. Aloft and beneath the vortex core, numerical simulations well reproduce the \$[{ k}_{h}^{- 5/ 3} { k}_{h}^{- 2} ] \$ scaling law of horizontal scales for the vertical derivative of temperature that is observed in situ inside the layering, whatever the background stratification. Such a result stems from the tracer-like behaviour of the vortex stretching component and previous studies have shown that spectra of tracer fields can be steeper than \$- 1\$, namely in \$- 5/ 3\$ or \$- 2\$, if the advection field is very compact spatially, with a \$- 5/ 3\$ slope corresponding to a spiral advection of the tracer. Such a scaling law could thus be of geometric origin. As for the kinetic and potential energy, the \${ k}_{h}^{- 5/ 3} \$ scaling law can be reproduced numerically and is enhanced when the background stratification profile is strongly variable, involving sharp jumps in potential vorticity such as those observed in situ. This raises the possibility of another plausible mechanism leading to a \$- 5/ 3\$ scaling law, namely surface-quasi-geostrophic (SQG)-like dynamics, although our set-up is more complex than the idealized SQG framework. Energy and enstrophy fluxes have been diagnosed in the numerical quasi-geostrophic simulations. The results emphasize a strong production of energy in the oceanic submesoscales range and a kinetic and potential energy flux from mesoscale to submesoscales range near the critical levels. Such horizontal submesoscale production, which is correlated to the accumulation of thin vertical scales inside the layering, thus has a significant slow dynamical component, well-captured by quasi-geostrophy.

This work addresses the linear dynamics underlying the formation of density interfaces at the periphery of energetic vortices, well outside the vortex core, both in the radial and axial directions. We compute numerically the unstable modes of an anticyclonic Gaussian vortex lens in a continuously stratified rotating fluid. The most unstable mode is a slow mode, associated with a critical layer instability located at the vortex periphery. Although the most unstable disturbance has a characteristic vertical scale which is comparable to the vortex height, interestingly, the critical levels of the successively fastest growing modes are closely spaced at intervals along the axial direction that are much smaller than the vortex height.

Depth-dependent barotropic instability of short mixed Rossby–gravity (MRG) waves is proposed as a mechanism for the formation of equatorial zonal jets. High-resolution primitive equation simulations show that a single MRG wave of very short zonal wavelength and small to moderate amplitude is unstable and leads to the development of a largely barotropic, zonally symmetric flow, featuring a westward jet at the equator and extra-equatorial jets alternating in direction with latitude. At higher but still moderate ampli-tude, westward flow still prevails at the equator at depths of maximum horizontal velocity amplitude in the initial wave, but the long-term equilibrated state can also feature eastward ''superrotating'' jets at the equator near the depths of zero horizontal velocity in the initial wave. The formation of the superrotating jets in the simulations is found to be sensitive to the inclusion of the nontraditional Coriolis force in the equations of motion. A linear theory is used to demonstrate the existence of exponentially growing horizontally non-divergent perturbations with a dominant zonally symmetric zonal velocity component. An argument for the sense and positioning of the jets relative to the equator is given in terms of inertial instability and the meridional mixing of planetary vorticity by the small zonal-scale components of the linearly unstable modes. In the long time evolution of the flow, if the amplitude of the westward equatorial jet becomes too great, zonally symmetric inertial instability limits the growth of the jets, and inertial adjustment leads to the homogenization of potential vorticity in latitude and depth around the equator.

Equatorial observations in the Atlantic show three distinct vertical scales: quasi-barotropic eastward Extra-Equatorial Jets (EEJ), Equatorial Deep Jets (EDJ) of scale 500-800 m, and a smaller scale signal (50-100 m) of thin layers of well-mixed tracer fields. In the combined system of jets, westward EDJ correspond to zero-Potential Vorticity (PV) "niches," inside of which most of the thin well-mixed layers are found. Because of its correlation with zero-PV niches, the formation of layers is interpreted as due to inertial instability. The latter encompasses inertial barotropic instability due to meridional shear (either steady or parametric), baroclinic symmetric instability due to sloping isopyenals and vertical velocity shear, and effective-beta inertial instability due to the curvature of a westward jet at the equator. In very high resolution numerical simulations, where equatorial deep jets of 500-800 m vertical scale are produced, density layering is observed with a characteristic depth of mixing of about 50 m. A statistical analysis reveals that the well-mixed layers are located in zones of marginal inertial stability, mainly due to the vertical shear of zonal velocity and curvature of westward jets and therefore points toward a baroclinic symmetric instability mechanism and an effective-beta inertial instability.

The available meridional sections of zonal velocity with high vertical and meridional resolution reveal tall eastward jets at 2N and 2S, named the extra-eqaatorial jets (EEJ), straddling the stacked eastward and westward jets of smaller vertical scales right at the equator, the so-called equatorial deep jets (EDJ). In contrast to the semi-annual to interannual fluctuations in the zonal velocity component, the measured meridional velocity component is dominated by intraseasonal period. We argue here that the formation mechanism for both types of jets is linked to the intraseasonal variability in meridional velocity and the associated wave motions. A process study is complemented by high resolution primitive equation simulations based on a realistic background stratification and an oscillating forcing inside the western boundary layer. The forcing confined to the upper 2500 in excites a spectrum of waves, including a baroclinic short Mixed Rossby-Gravity (MRG), whose instability leads to the formation of the EDJ and short barotropic Rossby waves, whose instability gives rise to the EEJ. The modeled EEJ and EDJ response is confined to the same depth range as the forcing. Potential vorticity is homogenized within specific depth ranges of westward EDJ and is found to be latitudinally confined between 2N and 2S by the EEJ. The combined EDJ and EEJ increase lateral mixing at the equator but also act as barriers at +/-2 degrees of latitude.

Low-frequency variations of the large-scale ocean circulation in the Atlantic are reconstructed from NODC pentadal anomalies of temperature and salinity from 1955 to 1998 based on hydrographic data, in addition to atmospheric reanalysis surface forcing. Diagnostic ocean circulations are estimated from simple methods using dynamical model integrations: namely diagnostic, robust diagnostic, and short prognostic. Mean transports of heat and mass are sensitive to the method and model configuration, but their decadal variability is much more coherent and does not depend explicitly on the variations of the surface forcing, its influence being imprinted in the thermohaline structure. Multidecadal variations are of the order of 20%, with large transports in the subpolar gyre in the early 1960's and mid 1990's, and low values in the mid 1970's. By reducing the influence of subgrid-scale parameterizations and surface forcings, these methods offer alternatives to exhaustive GCM simulations.

The stability of mixed Rossby gravity (MRG) waves has been investigated numerically using three-dimensionally consistent high-resolution simulations of the continuously stratified primitive equations. For short enough zonal wavelength, the westward phase propagating MRG wave is strongly destabilized by barotropic shear instability leading to the formation of zonal jets. The large-scale instability of the zonally short wave generates zonal jets because it consists primarily of sheared meridional motions, as shown recently for the short barotropic Rossby wave problem.Simulations were done in a variety of domain geometries: a periodic re-entrant channel, a basin with a short MRG wave forced in its western part and a very long channel initialized with a zonally localized MRG wave. The characteristics of the zonal jets vary with the geometry. In the periodic re-entrant channel, barotropic zonal jets dominate the total flow response at the equator and its immediate vicinity. In the other cases, the destabilization leads to zonal jets with quite different characteristics, especially in the eastward group propagating part of the signal. The most striking result concerns the formation of zonal jets at the equator, alternating in sign in the vertical, with vertical scale short compared to the scale of the forcing or initial conditions.A stability analysis of a simplified perturbation vorticity equation is formulated to explain the spatial scale selection and growth rate of the zonal jets as functions of the characteristics of the basic state MRG wave. For both types of zonal jets, the model predicts that their meridional scales are comparable to the zonal scale of the MRG wave basic state, while their growth rates scale as μ Fr |k|, where Fr is the Froude number of the meridional velocity component of the basic state and k its non-dimensional zonal wavenumber. The vertical scale of the baroclinic zonal jets corresponds to the dominant harmonic ppeak of the basic state in the fastest growing mode, given by ppeak≈0.55k2. Thus, the shorter the zonal wavelength of the basic state MRG wave, the narrower the meridional scale of the zonal jets, both barotropic and baroclinic, with the vertical scale of the baroclinic jets being tied to their meridional scale through the equatorial radius of deformation, which decreases as the square root of the vertical wavenumber. The predictions of the spatial scales are in both qualitative and quantitative agreement with the numerical simulations, where shorter vertical scale baroclinic zonal jets are favoured by shorter-wavelength longer-period MRG wave basic states, with the vertical mode number increasing as the square of the MRG wave period.An Appendix deals with the case of zonally long and intermediate wavelength MRG waves, where a weak instability regime causes a moderate adjustment involving resonant triad interactions without leading to jet formation. For eastward phase propagating waves, adjustment does not lead to significant angular momentum redistribution.

Master 2 Physique Océan Atmosphère Question posée: quelle est la dynamique de la pycnocline et comment cette structure peut être reliée au forçage du vent
Arnaud David Sous la direction de Richard Schopp 2008

Antarctic Intermediate Water (AAIW) occupies the intermediate horizon of most of the world oceans. Formed in the Southern Ocean, it is characterized by a relative salinity minimum. With a new, denser in situ National Oceanographic Data Center dataset, the authors have reanalyzed the export characteristics of AAIW from the Southern Ocean into the South Pacific Ocean. These new data show that part of the AAIW is exported from the subpolar frontal region by the large-scale circulation through an exchange window of 10 degrees width situated east of 90 degrees W in the southeast corner of the Pacific basin. This suggests the origin of this water to be in the Antarctic Circumpolar Current. A set of numerical modeling experiments has been used to reproduce these observed features and to demonstrate that the dynamics of the exchange window is controlled by the basin-scale meridional pressure gradient. The exchange of AAIW between the Southern and Pacific Oceans must therefore be understood in the context of the large basin-scale dynamical balance rather than simply local effects.

From a numerical simulation of the Atlantic Ocean, Jochum and Malanotte-Rizzoli provide evidence that the equatorial subsurface countercurrents can be triggered by tropical instability waves through eddy-mean flow interactions in a low-Rossby-number regime. Adapting the transformed Eulerian mean formalism to a shoaling jet, they propose eddy heat fluxes to be the driving mechanism for the subsurface countercurrents. Here it is shown that such a formalism relying on the existence of a residual meridional streamfunction cannot be applied to a shoaling jet, so that the eddy heat fluxes term in the zonal momentum equation cannot be rigorously justified. Moreover, the role of the zonal pressure gradient that was dropped in their study needs to be reassessed. Despite this mathematical questioning of Jochum and Malanotte-Rizzoli's framework, the authors agree with them that eddy heat fluxes may contribute to the dynamics of the subsurface countercurrents.

The deep equatorial track of the world ocean is subject to intense zonal flow fields that still remain to be better understood. Inertial instability has been invoked to explain some of its features. Here we present possible in situ imprints of such a mechanism in the equatorial Atlantic Ocean below the thermocline. We analyse the observed pattern of homogeneous density layers of 50 - 100 m vertical scale, which are characterized by a large meridional coherency up to 2degrees of latitude, a concentration in the vicinity of the equator and foremost a vertical localization within regions of well-mixed angular momentum ( westward jets). These distinctive properties suggest inertial instability to be a plausible mechanism for this extended layering. Numerical simulations forced by a time-oscillating shear reproduce the observed density layering characteristics. The prescription of deep jets in the background flow controls the vertical localization of the layering inside westward jets.

A fully three-dimensional primitive equation simulation is performed to "reunite" the local equatorial dynamics of the subsurface countercurrents (SCCs) and thermostad with the large-scale tropical ventilated ocean dynamics. It captures (i) the main characteristics of the equatorial thermostad, the SCCs' location and their eastward evolution, and the potential vorticity budget with its equatorial homogenization to zero values and (ii) the large-scale meridional shoaling of the thermocline equatorward. It supports the idea that the two-dimensional Hadley cell mechanism proposed by Marin et al. is a candidate able to operate in a fully three-dimensional ocean. The main difference between the 2D Hadley cell mechanism and the oceanic 3D case is that for the 3D case the large-scale meridional velocity at zeroth order is geostrophic, while the cell mechanism is a next-order, small-scale mechanism. A detailed budget of the zonal momentum equation is provided for the ageostrophic dynamics at work in the SCCs. The mean meridional advection and the Coriolis term dominate, discounting the possibility that lateral eddies play a major role for the SCCs' creation. A 31/2-layer idealized ventilation model, calibrated to the three-dimensional simulation parameters, is able not only to capture the tropical density structure, but also to isolate the main controlling factors leading to the triggering of the equatorial secondary cells with its associated jet and thermostad, namely, the shoaling of the equatorial thermocline because of low potential vorticity injection at distant subduction latitudes. It is also shown that equatorial recirculation gyres play a quantitative role that may be of the same order of magnitude as ventilation from higher latitudes.

Sensitivity tests are performed to assess the respective influences of the large-scale ventilation and of the near-equatorial winds on the dynamics of the the subsurface countercurrents (SCCs) and thermostad. They show that the intensity of the inertial jets is a function of the potential vorticity (PV) values at subduction and that stronger jets are favored by low PV injection, forced in the authors' framework either by a deep mixed layer at subduction and/or by an injection of PV at lower latitudes. Such circumstances lead to a strong meridional shoaling of the thermocline near the equator. The resulting inertial jets occur at about 3°N in the western part of the basin and are the poleward limit of a near-0 PV region and of an equatorial thermostad. A necessary condition for the existence of inertial jets is that the equatorial wind fetch is large enough, otherwise only weak time-mean eastward currents are produced by a nonlinear rectification of instability waves farther away from the equator. The presence of a North Equatorial Countercurrent does not constitute a barrier for equatorward motions within the lower thermocline, and inertial jets are still controlled by the meridional slope of the SSCs' layer setup through the establishment of tropical PV pools predicted by ventilation theory.

Potential vorticity redistribution across the equator have been diagnosed both in in situ observations (Send et al. JPO2001) and in numerical basin simulations of equatorial deep flows. Zonally symmetric inertial instability is known to create such redistribution but preferentially at the smallest vertical scales. In this study, we explore the effects of zonal assymmetry on this issue of vertical scale selection. The equilibration of a prescribed meandering westward current is examined in an equatorial channel using a primitive equations model without explicit vertical diffusion and for the case of a stratified flow. Such a prescribed flow exhibits regions where relative vorticity is opposite to planetary vorticity, a necessary condition for symmetric inertial instability. For our zonally asymmetric basic state, we indeed observe for all vertical scales a growth of perturbations that present a zonally invariant component that is moreover symmetrical about the equator. Smallest vertical scales grow the fastest initially but saturate rapidly. The final state is found to be dominated by the largest vertical scales compatible with the domain geometry. More importantly, density layering is ubiquituous for a westward meandering current along with cross-equatorial potential vorticity fluxes.

- Jun 2001

Uncertainties in the surface wind field have long been recognized as a major limitation in the interpretation of results obtained by oceanic circulation models. Surface winds over the global oceans are measured by scatterometry since ERS-1 launch in August 1991 by the European Space Agency and its follow-on ERS-2 launched in April 1995. Despite the stop of ERS-2 scatterometer operations in January 2001, scatterometry measurements were not interrupted since the National Aeronautic and Space Administration QuikSCAT scatterometer launched in June 1999 still operates. Scatterometer observations thus cover more than 10 years, providing an unprecedented high resolution surface wind global data-set. The objective of this study is twofold: firstly to investigate the sensitivity of an ocean numerical model to wind forcing, and secondly to validate, by the way, the European Center for Medium Range Weather Forecasts wind re-analysis often used as the momentum forcing field in numerical experiments. The CLIPPER model used in this study aims at modelizing the Atlantic Ocean at high resolution. Two experiments were achieved with 13o resolution and an annual forcing: one with the wind from the ECMWF reanalysis, and the other with the wind from the scatterometry measurements of the ERS satellites. The results comparison enables to investigate the role of the wind in several key topics of the ocean circulation. The study focuses on the dynamic and thermohaline structures, analyzing their seasonal variability and their differences from in situ observations. The model suggests that the strength of the trade winds is more realistic in the ERS wind stress field. The major consequences are that the intensity of the subtropical gyres are weaker and that the thermohaline structure of the waters is better simulated. The reason for which ECMWF and ERS wind stress fields differ is discussed.

- Jun 2001

A fully three-dimensional Primitive Equations simulation is performed to ``reunite'' the local equatorial dynamics of the subsurface Counter Currents (SCCs) and thermostad with the large-scale tropical ventilated ocean dynamics. It captures (i) the main characteristics of the equatorial thermostad, the SCCs location and their eastward evolution as well as the Potential Vorticity budget with its equatorial homogenization to zero values; (ii) the large-scale meridional shoaling of the thermocline equatorward. It supports that the two-dimensional Hadley cell mechanism proposed by Marin et al. (2000) is a candidate able to operate in a fully three-dimensional ocean. % The main difference between the 2D Hadley cell mechanism and the oceanic 3D case is that for the 3D case the large-scale meridional velocity at zeroth order is geostrophic, while the cell mechanism is a next order, small-scale mechanism. A detailed budget of the zonal momentum equation is provided for the ageostrophic dynamics at work in the SCCs. The mean meridional advection and the Coriolis term dominate, discarding the possibility that lateral eddies play a major role for the SCCs creation. % A 3-1/2 layer idealized ventilation model, calibrated to the 3-dimensional simulation parameters, is able not only to capture the tropical density structure, but also to isolate the main controlling factors leading to the triggering of the equatorial secondary cells with its associated jet and thermostad, namely the shoaling of the equatorial thermocline due to low potential vorticity injection at distant subduction latitudes. It is also shown that equatorial recirculation gyres play a quantitative role which may be of the same order of magnitude as ventilation from higher latitudes.

The GyroScope project started with the new millennium, on January 2nd, 2001. Nine laboratories in four countries are collaborating to develop a component of an in situ observing system of ocean variability. The project is an initial contribution to the international ARGO project, which plans to deploy a global array of some 3000 autonomous profiling floats to observe large scale ocean variability.

Two independent data sets are used to diagnose the wind effect on the mesoscale activity in the North Atlantic Ocean. The oceanic surface variability is described with TOPEX/Poseidon sea surface height measurements from October 1992 to September 1997. Spatial extensions and temporal variations of high mesoscale activity are compared with the zonal and meridional components of the ERS-1 wind stress, the Ekman pumping, and the zonal Sverdrupian velocity. Regions with high mesoscale surface variability seem to be correlated to regions with eastward Sverdrupian velocities. When the Sverdrupian velocity is eastward and increases with time, the mesoscale activity is intensified, indicating a growth of instability rates. Theoretical and numerical results based on the interplay of barotropic eastward Sverdrup flows and westward propagation of long Rossby waves suggest that the wind controls western regions where baroclinic instability is favored. Interactions between the eddy field and the mean circulation are therefore analyzed to try to extract the instability mechanism responsible for the growth of the mesoscale activity along the Gulf Stream and the North Atlantic Current. Our results seem to suggest that the seasonal changes of mesoscale activity, associated with eastward currents, are linked to seasonal changes of the eastward Sverdrupian velocity.

The motion of fluid contained between two concentric spherical surfaces is analysed in the limit of strong rotation appropriate to large scale flows and arbitrary gap width. To do so, the dynamical equations are written in the natural cylindrical co-ordinate system that gives a central role to the axis of rotation. The case of a homogeneous fluid allows us to give a general solution of the inviscid, steady flow when sources and sinks have prescribed boundary distributions. Fluid can cross the equatorial plane without breaking rotational constraints provided the source-sink forcing is antisymmetric. However the cylindrical surface tangent to the inner sphere at the equator is singular and calls for higher order inertial and/or viscous effects. No specific solution is obtained in the stratified case, instead a number of integral constraints along the axis of rotation are derived allowing us to relate the interior motion to the surface forcing distributions. The unsteady low frequency waves with Taylor column-like motions are obtained exactly and we extend the non dispersive limit of classical Rossby wave theory in concentric spheres of arbitrary gap width. In the stratified case, a new mode that has no counterpart in the classical, shallow fluid theory is found at the equator.

The effect of the wind on large scale circulation is analysed to locate the different dynamical regimes observed in the ocean on a global scale. It is shown that the wind plays a major role in shaping the circulation of the upper part of the ocean. On the basis of planetary potential vorticity dynamics allowing isopycnals to have large vertical excursions, one is able to locate the high energetic regions associated with jet like structures within the ocean, to locate the major convection regions and to give some insight into the permanent thermocline structure. The theory is based on the interaction of the barotropic zonal Sverdrup current and the non-linear baroclinic non dispersive Rossby wave. With the aid of observed wind fields, we show that, within regions where Rossby waves propagate to the West and Sverdrup type dynamics prevail, low eddy active regions and weak pycnoclines are observed. On the contrary, within regions where Rossby waves are advected to the East by the wind-induced Sverdrup zonal current, high meso-scale variability is observed associated with strong jets. Strong thermoclines are present within such regions. Observations, theory and numerical quasi-geostrophic modelling converge to the same conclusion: the Sverdrup wind mode controls the eddy active regions and favours baroclinic instability to act in these regions. The following simple observational analyses strongly support the analytical theories based on potential vorticity pools and ventilated thermocline.

It is well known that the widely used powerful geostrophic equations that single out the vertical component of the Earth's rotation cease to be valid near the equator. Through a vorticity and an angular momentum analysis on the sphere, we show that if the flow varies on a horizontal scale L smaller than (Ha)1/2 (where H is a vertical scale of motion and a the Earth's radius), then equatorial dynamics must include the effect of the horizontal component of the Earth's rotation. In equatorial regions, where the horizontal plane aligns with the Earth's rotation axis, latitudinal variations of planetary angular momentum over such scales become small and approach the magnitude of its radial variations proscribing, therefore, vertical displacements to be freed from rotational constraints. When the zonal flow is strong compared to the meridional one, we show that the zonal component of the vorticity equation becomes (2Ω.Δ)u1 = g/ρ0)([partial partial differential]ρ/a[partial partial differential]θ). This equation, where θ is latitude, expresses a balance between the buoyancy torque and the twisting of the full Earth's vorticity by the zonal flow u1. This generalization of the mid-latitude thermal wind relation to the equatorial case shows that u1 may be obtained up to a constant by integrating the ‘observed’ density field along
the
Earth's
rotation
axis and not along gravity as in common mid-latitude practice. The simplicity of this result valid in the finite-amplitude regime is not shared however by the other velocity components.

Oceanic Trapped Taylor-Proudman columns by topography

A simple Sverdrup-type two-layer model that allows the outcropping of isopycnals is forced by wind stress, is completed with a frictional western boundary layer, and is investigated along the zero wind-stress curl line separating the subpolar gyre from the subtropical gyre. The study focuses on the different cross-gyre flow patterns. -from Author

Simulations of the wind-driven Ocean circulation, carded out with an eddy-resolving quasi-geostrophic numerical model, and symmetric, idealized wind forcing have a large-scale structure that is predicted wen by the steady nonlinear theory of Rhines and Young. The sharp jet and inertial recirculation am often confined weft inside the region of closed hyperbolic characteristics, defined by that theory, and hence do not affect the Sverdrup-dynamics part of the gyre. The characteristics make possible simple predictions about the development of the circulation, including time dependence and eddy stirring. By tilting the line of vanishing Ekman pumping away from the east-west orientation (as it is tilted in the North Atlantic, and less so the North Pacific), we explore a family of circulations. As the tilt of the wind held is increased, characteristics originating at the eastern boundary begin to thread through the energetic region occupied by the free jet. Then, extensive new branches of eddy-driven f...

An interpretation in terms of planetary waves is proposed, which sheds light on the dynamics underlying the large-scale cross-gyre geostrophic flow recently developed in a two-layer ventilated thermocline model. The cross-gyre communication flow is the result of an arrested nondispersive baroclinic Rossby wave in the presence of zonal Sverdrup transport along the line of vanishing Ekman pumping. A baroclinic adjustment is described in which a resting ocean settles to a steady communicating solution.

Several mechanisms are proposed to explain the northward ﬂow observed at middepth in the eastern North Atlantic. These mechanisms are based on the two forcings that can set the ocean in motion: wind forcing on the one hand, andthermodynamical forcing on the other hand.In the ﬁrst mechanism that is based on the hypothesis of the ventilated thermocline, the middepth layer in the subtropical gyre is set in motion by the Ekman pumping in the subpolar gyre where this layer outcrops. Cross-gyre communication, revealing a blocking condition of a nondispersive baroclinic Rossby wave by a barotropic zonal current at both gyres junction, enables to perform a time-dependent adjustment of the stationary solution found, from a resting ocean. A ﬂat bottom ventilated model has also been performed in the subtropical gyre, showing other characteristics in the eastern North Atlantic. The second part of the study mainly concerns the forcing that can result from double diffusion processes at the base of the Mediterranean intrusion into the Atlantic ocean. This mechanism allows salt to fall out and create
locally horizontal density gradients which, in turn, enable to generate geostrophic shearing currents. A northward ﬂow, based on this dynamics, is performed by a release of salt from a source located on the eastern coast of
this basin, simulating the Mediterranean supply.

A mechanism is proposed, based on the assumption of ventilation, to explain the middepth northward flow observed in the North Atlantic. The main feature of the solution is that the outcropping line of an intermediate layer at high latitudes is uniquely specified by the condition that the middepth waters of the subtropical gyre may be “sucked up” by the positive Ekman pumping of the subpolar gyre.
This model is consistent with several characteristic features of the circulation in that region such as its vertical structure, the greater northward extension of the warm waters in the eastern ocean and the shape of the large scale Mediterranean water plume. In a variation of the model, the observed isopycnal slopes along the eastern coast are included in the analysis; this implies the existence of eastern boundary layers.

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