Dynamics and Stability of Multiple Jets in Geophysical Flows

Abstract

The effect of rotation on the stability of multiple jets in planetary atmospheres is system- atically investigated. Typically in Jovian planetary atmospheres, multiple zonal jets have been observed and their morphology has been systematically studied. The formation of jets has always been viewed as a nonlinear problem where most work has followed from the ideas of potential vorticity (PV) homogenization or turbulent mixing on a β-plane. In our present work, we have aimed to look at the linear stability of multiple jets in a geophysical fluid, and hope to add further insight into the observed jet profiles in β-plane turbulence. In addition, we also study the evolution and life-cycle of these jets as they interact with each other in a non linear fashion. We begin with the linear stability of the \Bickley jet" using the linearized shallow water quasigeostrophic (QG) equations. We have included a finite deformation radius in our calculations to partially mimic the effects of compressibility. A family of synthetically generated velocity profiles with east-west jets are then studied. In particular, a variety of flow configurations with two jets have been considered with a parameter sweep across jet separation, relative jet strength and thickness. As a broad observation, it is noted that an asymmetric east-west jet profile with a stronger and sharper eastward jet is the most stable of all the profiles considered, and a finite deformation radius further stabilizes such profiles. More realistic jet profiles have also been considered and the role of a finite deformation radius in stabilizing such jets is elucidated. We also examined the nonlinear evolution of multiple jets in a periodic domain and in a channel geometry, as we undertake freely decaying long time simulations of the governing QG equation. As per the \Selective Decay" principle we observe that arbitrary initial conditions approach the flow configuration of the prescribed \suitable end states". In addition, we have shown how a finite deformation length scale modifies these \suitable end states". As a broad observation, we have noted that a linearly unstable jet flow configuration, in the presence of β, breaks down into turbulence and reforms into a more asymmetric jet profile with a stronger and sharper eastward jet. The inclusion of a finite deformation length scale in our calculations, is observed to suppress such jet formation. Similar numerical experiments have been performed in a channel and the results have been compared. Chiefly, for the end states, the nature of the observed jet asymmetry is reversed, i.e., the westward jets are observed to be stronger in a channel.