Richard Schopp

Destabilization of mixed Rossby gravity waves and the formation of equatorial zonal jets.

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 xs221D 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.

Slow quasigeostrophic unstable modes of a lens vortex in a continuously stratified flow

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.

Extended deep equatorial layering as a possible imprint of inertial instability

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.

Dynamics of the combined extra-equatorial and equatorial deep jets in the Atlantic

The available meridional sections of zonal velocity with high vertical and meridional resolution reveal tall eastward jets at 2N and 2S, named the extra-equatorial 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 m 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.

Three-Dimensional Dynamics of the Subsurface Countercurrents and Equatorial Thermostad. Part I: Formulation of the Problem and Generic Properties

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 largescale 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, smallscale 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 3 ‰-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.

Three-dimensional dynamics of the subsurface countercurrents and equatorial thermostad. Part II: Influence of the large-scale ventilation and of Equatorial winds

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 8N 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.

Tracer Stirring Around a Meddy : The Formation of Layering

AbstractThe dynamics of the formation of layering surrounding meddy-like vortex lenses is investigated using primitive equation (PE), quasigeostrophic (QG), and tracer advection models. Recent in situ data inside a meddy confirmed the formation of highly density-compensated layers in temperature and salinity at the periphery of the vortex core. Very high-resolution PE modeling of an idealized meddy showed the formation of realistic layers even in the absence of double-diffusive processes. The strong density compensation observed in the PE model, in good agreement with in situ data, suggests that stirring might be a leading process in the generation of layering. Passive tracer experiments confirmed that the vertical variance cascade in the periphery of the vortex core is triggered by the vertical shear of the azimuthal velocity, resulting in the generation of thin layers. The time evolution of this process down to scales of O(10) m is quantified, and a simple scaling is proposed and shown to describe preci...

Equatorial Zonal Jet Formation through the Barotropic Instability of Low-Frequency Mixed Rossby–Gravity Waves, Equilibration by Inertial Instability, and Transition to Superrotation

Abstract 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 amplitude, 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 ...

Cyclones and Anticyclones in Seismic Imaging

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.

Comments on “A New Theory for the Generation of the Equatorial Subsurface Countercurrents”

Abstract 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.