Fronts in differentially rotating stratified fluids

Abstract

This paper reports an experimental investigation on baroclinic fronts, as generated during the spin-up of a two-layer salt-stratified fluid in a cylindrical container. The stability of these fronts is considered as a function of the rotational Froude number, defined as Fr= 4(Omega^2*R^2)/(g′H) and dissipation denoted by the ratio of the Ekman spin-up time and rotation time of the disk, d= sqrt((nu*Omega)(/(H*delta(Omega)) (here g′ = g*Delat(rho) /mean(rho) is the reduced gravity with mean(rho) the mean fluid density and delta(rho) the density jump, H half layer depth, Omega the background rotation frequency, delta(Omega) the increase in rotation, and nu the fluid viscosity). As a function of these two parameters the different stability regimes of the spin-up front range from Kelvin Helmholtz instability, centrifugal instability to regular and chaotic baroclinic unstable flow. In the baroclinic unstable regimes, waves are radiated by the front in a manner that is reminiscent of the spontaneous emitted inertia gravity waves reported by Plougonven and Snyder (GJR 2005). The interaction of these waves with the large-scale baroclinic waves may lead to local intense mixing and the rapid formation of intense cyclonic vortices, showing evidence of a downscale energy process in geostrophic turbulence. We qualitatively characterize the different stability regimes and discuss them in the light of former results on differential spin-up flows in inmiscible fluids and former results on spin-up fronts in linearly stratified fluids.