Effects of topography on the beta-drift of a baroclinic vortex

The propagation of compact, surface-intensified vortices over a topographic slope on the beta-plane is studied in the framework of a two-layer model. A perturbation theory is derived for a circular vortex in the upper layer with the lower layer at rest as a basic state. An integral momentum balance for the upper layer is used to obtain expressions for the velocity of the vortex center assuming the flow is quasi-stationary to leading order. This approach allows the calculation of the lower-layer flow pattern as a function of the interface shape and the slope orientation. The essential part of the lower-layer flow pattern is elongated dipolar gyres generated by the cross-slope vortex drift which remains nearly the same as in the reduced-gravity approximation, although it is slightly modified when the slope is not constant. Therefore, the major effect of the lower-layer flow is an additional along-slope propagation which is proportional to the cross-slope speed and the ratio of the interface slope to the topographic slope. Both along-slope and cross-slope drift components are found to be also affected by the slope variation

Critical effects of a tall seamount on a drifting vortex

The initial-value problem for the evolution of an isolated vortex encountering a tall seamount during its westward beta-drift is studied within an equivalent-barotropic model, that is generalized to allow for the intersection of the layer interface with a sloping bottom. Given the Rossby radius and linear wave speed in the model, the parabolic shape of a seamount top and initial potential vorticity profile in the vortex core, the outcome is controlled by the vortex sign and a number of parameters: the seamount radius and height of penetration into the active layer, the radius and intensity of the vortex, the initial offset of the vortex center relative to the seamount, the Ekman layer depth over the seamount top, and the momentum lateral diffusion coefficient. Here we consider regimes for narrow seamounts where cyclonic vorticity generated in the water column swept off the top of the seamount plays a negligible role. The most significant effect on the vortex evolution is provided by a topographically induced anti-cyclonic circulation that is formed after squashing of water column replaced over the top of the seamount by the approaching vortex. The Geostrophic Vorticity intermediate model is used for numerical experiments. When the area of penetration is small and the topographic anticyclone is weak, the vortex drifts either predominantly westward north of the seamount or rotates around the seamount which is explained by presence of a separatrix in a simple kinematic model. For a larger area of penetration and stronger topographic anticyclone, violent interactions result in substantial deformations of the vortex core and loss of the material from the vortex periphery that leads to anomalous transport and diffusion. Vortex capture over the seamount is found in one range of parameters

Stabilization of Isolated Vortices in a Rotating Stratified Fluid

The key element of Geophysical Fluid Dynamics—reorganization of potential vorticity (PV) by nonlinear processes—is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies

Ageostrophic instabilities in a baroclinic flow over sloping topography

The ageostrophic normal modes of a spatially uniform, vertically sheared flow along a sloping bottom are considered in two layers underneath a deep motionless third layer (two-and-half layer model). The variations of the layer thickness are assumed to be small to derive the six-order dispersion relation with constant coefficients valid for finite Froude number typical for oceanic currents. The dispersion curves for the Rossby waves and inertia-gravity waves (IGW) are investigated to identify different types of instabilities occurs if there is a pair of wave components which have almost the same Doppler-shifted frequency related to crossover of the branches when the Froude number increases. Ageostrophic instabilities due to a resonance between the IGW modes and the Rossby wave in either lower, or middle layer, are described. In both cases the growth rate and the width of the unstable wavenumber window are shown to be proportional to the square root of the corresponding gradient of the layer thickness. These powerful types of ageostrophic instability can coexist together (and with Kelvin-Helmgoltz instability) and may play an important role in mixing processes in geophysical fluids

Generation of inertia-gravity waves by pulsating lens-like axisymmetric vortices

We consider interactions between the two most important components of the atmosphere and ocean dynamics: slowly evolving vortical motion and inertia-gravity waves in rotating stratified axisymmetric flows. Any steady axisymmetric solution for a finite volume anticyclonic vortex with outcropping isopycnals is known to correspond to a set of self-similar analytical time-periodic pulson solutions assuming flows in surrounding fluid is negligible. Here we analyze the flow patterns generated in homogeneous fluid below stratified pulsating lens-like vortex and its feedback on the upper layer vortex

Deep cyclogenesis by synoptic eddies interacting with a seamount

Strong deep eddies with cyclonic vorticity greater than 0.2 f0 were detected using an array of bottom current and pressure measurements in the Kuroshio Extension System Study (KESS) in 2004–2006. Daily maps showed these deep eddies developed locally. As in the Gulf Stream, meandering of the upper baroclinic jet generates deep cyclones and anticyclones by stretching and squashing the lower water column. However, unlike the Gulf Stream, the smaller vertical stretching and greater water depth in the Kuroshio Extension limits the relative vorticity generated by this vertical coupling process to about 0.1 f0. In the deep Kuroshio Extension the strong cases of vorticity generation and cyclone development are related to stretching driven when water columns are advected off isolated seamounts in the region. The large observed values of relative vorticity are consistent with a straightforward calculation of deep layer potential vorticity conservation.A barotropic model is used to illustrate the topographic generation of cyclones by ambient currents in synoptic eddies. Positive potential vorticity filaments also develop during the cyclogenetic process with width LR = O(20 km), where LR is the topographic Rhines scale, and travel anticyclonically around the seamount. Observational evidence lends support to the existence of submesoscale filaments, insomuch as current meter records near the flanks of seamounts exhibited bursts of eddy kinetic energy when bandpass-filtered between the inertial period and eight days

Evidence of Vertical Coupling between the Kuroshio Extension and Topographically Controlled Deep Eddies

Strong energy in the 30–60 day band was observed using 39 deep pressure and current records from the Kuroshio Extension System Study (KESS). Energy in this band accounted for 25–50% of the total deep-pressure variance and was strongest under the Kuroshio Extension jet axis. Often, deep-pressure anomalies propagated into the region from the north-northeast and locally intensified as they passed under and interacted with the Kuroshio Extension. The topographically controlled deep-pressure anomalies translate nearly along lines of constant f/H. Statistically significant coherence between 30–60 day upper- and deep-ocean streamfunction anomalies demonstrated that there was strong vertical coupling in that time band. Twenty-five percent of the total upper-ocean streamfunction variance was contained within the 30–60 day band near the Kuroshio Extension. Joint CEOFs of the upper- and deep-ocean streamfunctions revealed that near the axis of the Kuroshio Extension the phases were laterally offset alongstream, with the deep ocean leading the upper ocean. This arrangement is attributed to producing joint development of upper-ocean meanders and deep-pressure anomalies.A numerical process model simulated the interaction of barotropic TRWs with an eastward-flowing baroclinic jet. When the TRWs, used as a surrogate for topographically steered deep-pressure anomalies, passed under the jet, they intensified and upper-ocean meanders steepened, much like the observed interactions. The model illustrates how the interaction between TRWs and an eastward-flowing jet, at its simplest level, can reproduce many of the major traits of our observations. The Ocean General Circulation Model for the Earth Simulator also showed similar processes in the 30–60 day band in the KESS region. The strongest variance in the deep fields occurred under the Kuroshio Extension. Upper and deep low- and high-pressure anomalies propagated south southwestward across the Kuroshio Extension, with model phase speeds and wavelengths matching the KESS observations

Stabilization of Isolated Vortices in a Rotating Stratified Fluid

The key element of Geophysical Fluid Dynamics—reorganization of potential vorticity (PV) by nonlinear processes—is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies

Equilibration of Baroclinic Meanders and Deep Eddies in a Gulf Stream–type Jet over a Sloping Bottom

Spatiotemporal evolution of a small localized meander on a Gulf Stream–type baroclinically unstable jet over a topographic slope is investigated numerically using a three-dimensional, primitive equation model. An unperturbed jet is prescribed by a potential vorticity front in the upper thermocline overlaying intermediate layers with weak isentropic potential vorticity gradients and a quiscent bottom layer over a positive (same sense as isopycnal tilt) cross-stream continental slope. A series of numerical experiments with the same initial conditions over a slope and flat bottom on the β plane and on the f plane has been carried out. An initially localized meander evolves into a wave packet and generates deep eddies that provide a positive feedback for the meander growth. Meanders found growing over a flat bottom are able to pinch off resembling warm and cold core rings, while in the presence of a weak bottom slope such as 0.002, the maximum amplitudes of meanders and associated deep eddies saturate with no eddy shedding. In the flat bottom case, the growth rate is only 10% larger than in the weak slope case. Nevertheless, the bottom slope efficiently controls nonlinear saturation of meander growth via constraining the development of deep eddies. The topographic slope modifies the evolution of deep eddies and causes the phase displacement of deep eddies in the direction of the upper layer troughs/crests, thus limiting growth of the meanders. Behind the wave packet peak deep eddies form a nearly zonal circulation that stabilizes the jet in an equilibrated state. The main equilibration mechanism is a homogenization of the lower-layer potential vorticity by deep eddies. The width of the homogenized zone is narrower for a larger slope and/or on the β plane. These results have the following implications to the Gulf Stream dynamics: 1) maximum of the meander amplitudes increase as the topographic slope relaxes in qualitative agreement with observed behavior of the Gulf Stream, 2) the phase locking of the meanders with deep eddies underneath at the nonlinear stage agrees qualitatively with the observed structure of large amplitude cyclonic troughs at the central array, and 3) the increase of the barotropic transport on the warm side of the jet and the generation of the recirculation on the cold side of the jet is consistent with observations in the Gulf Stream system downstream of Cape Hatteras