DYNAMICS OF BAROCLINIC VORTICES IN A ROTATING, STRATIFIED FLUID - A NUMERICAL STUDY

This study deals with the instabilities that arise in the flow generat ed in a rotating tank by the evolution of a two-layer density stratifi ed fluid. Numerical investigations have been performed by direct simul ation of the Navier-Stokes equations for axisymmetric and fully three- dimensional flows. In the former case results have shown the attainmen t, in a very short time, of an equilibrium position and the formation of an anticyclonic structure in the upper Light layer and a cyclonic o ne in the lower layer, consistently with the observation of Griffiths and Linden. In the long term, however, the Ekman layer at the bottom d amps out the cyclone and a steady state with only an anticyclone in th e upper layer is reached. In three-dimensions the how is unstable to a zimuthal disturbances and the steady state is no longer achieved. In p articular a ring of cyclonic vorticity, surrounding the anticyclone, b y the combined effects of baroclinic and barotropic processes, breaks, entrains vorticity from the anticyclone and eventually forms vortex p airs. As observed by Griffiths and Linden the azimuthal wave number (n ) of the instability depends on the Richardson number (Ri) and the ra tio between the depth of the light fluid and the total depth (delta). However, since several modes, in addition to the most unstable, are am plified an initial perturbation whose energy is not equidistributed am ong the modes can lead to an instability with wave number different fr om the expected n. Finally, the analysis of the equation for the ener gy of the instability has shown that the instability is initially driv en by baroclinic effects, even for low values of delta. The barotropic source, in contrast, sets in only in the large-amplitude phase of the instability and its effect is larger when delta is small. (C) 1997 Am erican Institute of Physics.