On the equilibration of asymmetric barotropic instability

Harnik, N., Dritschel, D. G. and Heifetz, E. (2014), On the equilibration of asymmetric barotropic instability. Q.J.R. Meteorol. Soc.. doi: 10.1002/qj.2310      pdf file

In this work we comprehensively examine one of the most fundamental processes operating in the atmosphere and oceans: barotropic instability, which arises when both positive and negative PV gradients are present. We examine the evolution of a uniform anti-cyclonic PV strip (dark blue strip in movie below) adjacent to a PV staircase (yellow-red regions) on a barotropic β-plane. This is a modified Rayleigh-Kuo problem, in which the positive PV jump is divided into two steps, and the sum of these two positive jumps is larger than the negative jump. Unlike the symmetric Rayleigh problem, in which PV gradients eventually get wiped out, in the asymmetric profile, a positive PV jump remains which sustains waves throughout the evolution. This highly simplified problem thus   allows us to study the fundamental and complex interrelation between the mean flow, Rossby waves and vortices. We find a consistent pattern of behavior across a wide range of parameters defining the initial flow, beginning with a linear growth stage, a nonlinear cascade stage, and a subsequent equilibration stage. The following movie shows the evolution of one of the runs. The negative PV anomaly is initially distorted by the unstable growing waves, and subsequently breaks up into a street of negative vortices, which shear and pair while the dominant wavenumber of the interface undulations decreases. The vortices eventually get sheared out completely leaving a well mixed stable mean PV structure with waves. The movie also shows the rich evolution of filaments on the final PV interface, which form dragon-head like structures.

 

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