The Stratified Pulson

Abstract

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.