Adjustment of lens-like stratified axisymmetric vortices to pulsons

Abstract

A Lagrangian approach is formulated for rotating stratified axisymmetric flows. The moment of inertia for compact flows with finite energy is shown to oscillate with inertial frequency. In particular, any steady axisymmetric solution for a finite volume inviscid anticyclonic vortex with outcropping isopycnals corresponds to a set of self-similar analytical time-periodic pulson solutions with linear profile of radial velocity which is not affected by horizontal friction. The amplitude of pulsations with inertial frequency can be within a range limited by the intensity of the stationary vortex. If the initial conditions deviate from the pulson solution, inertiagravity waves propagate inside the vortex and may form shocks at the vortex edge calculated by a Lagrangian numerical model. After shocks dissipate due to small friction added near the edge, the solution tends to the pulson solution with linear radial velocity. © 2008 Springer.