The Stratified Pulson

Abstract

New analytical nonstationary circular eddy solutions of the nonlinear, reduced-gravity shallow-water equations in a multilayer stratified rotating ocean are presented. The new solutions extend previous "pulson" analytical solutions, which describe circular oscillating lenslike warm core eddies in a reduced-gravity homogeneous ocean on the f plane, to arbitrary stable vertical stratifications within surface as well as intermediate vortices. As a result, cyclonic as well as anticyclonic horizontal swirl velocities can coexist on different vortex layers within parts of an inertial period, while vertical distributions of the vortex mean tangential velocity resembling observed vertical velocity distributions of surface as well as intermediate lenslike vortices are obtained. The dynamics of a two-layer pulson is discussed and it is shown that, for nonnegligible lower-and upper-layer thickness, its total water transport substantially differs from the total water transport of the corresponding homogeneous pulson. In linearly stratified warm core vortices it is found that the amplitude of the temporal oscillation of the azimuthal velocity is maximum in the bottom layer and decreases toward the surface, while the mean azimuthal velocity is minimum in the bottom layer and increases toward the surface. In linearly stratified intermediate vortices it is found that the mean azimuthal velocity is no longer a monotonic function of the water depth: it is maximum at the top and at the bottom of the vortex and minimum at the vortex central depth. The new solutions add realism to known analytical vortex solutions and elucidate aspects of the observed complexity of geophysical vortex motions.

Abyssal undular vortices in the Eastern Mediterranean basin

“…3b). Notably, anticyclonic mesoscale vortical features characterized by similar radial structures of their tangential velocities describing internal undular oceanic vortices have been recently discovered as robust solutions of the non-stationary, nonlinear shallow-water equations on an f-plane [23][24][25][26] and also demonstrated as being persistent features of both oceanic and laboratory flow fields 27,28 . Remarkably, they are all characterized by the presence of (quasi) inertial pulsations, as those observed here to be significantly enhanced during vortical activity (Fig.…”

Frictionally Decaying Frontal Warm-Core Eddies

“…A prominent role in the theoretical investigation of geophysical frontal vortices has been played by the nonlinear, reduced gravity shallow water equations [18,20,[22][23][24][25][26].…”

“…Although these equations do not allow for the development of baroclinic instabilities or for the radiation of energy toward the interior ocean via internal waves propagation, their use enables to explain different characteristics of observed frontal vortices [18,20,[22][23][24][25][26]. Moreover, the possibility of expressing analytically the evolution of a broad class of geophysical frontal vortices using these equations represents a valuable way for testing the accuracy of numerical models for non-stationary, nonlinear, frontal phenomena of geophysical relevance [18,19,22,27].…”

“…Fundamentally, in the case of circular symmetry, the features emerging as analytical solutions in the reduced-gravity frame are characterized by inertial oscillations affecting both radial and tangential velocities and vortex's depth: The vortices contract and expand during an exact inertial period [22,25]. Note that, in these analytical solutions, the vortex's radial velocity field is constrained to be a linear function of the vortex's radius, while the azimuthal velocity field and the vortex's section can show a more complex shape [25,26]. A More complex behavior is also possible for frontal vortices characterized by elliptic sections: In this case subinertial and superinertial oscillations emerge as a part of the corresponding analytical solution (see [22]).…”

Secularly growing oscillations in a stratified rotating fluid

“…Idealized flow models in which the velocity components vary linearly with one or more of the spatial coordinates have been applied in many contexts. Such models have led to wave and vortex solutions of the nonlinear shallow-water equations, [1][2][3][4] the multi-layer reduced shallow-water equations, 5,6 the Euler equations, 7 and the Boussinesq equations for a stratified fluid under the hydrostatic approximation. 8 Such models have also been applied to sea-breezes, 9 horizontal natural convection along a thermally perturbed lower surface, 10 thermal convection between two conducting horizontal boundaries, 11 katabatic flow along a differentially cooled slope, 12 and the flow in typhoons.…”