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.