Generation of zonal flows through symmetry breaking of statistical homogeneity
Authors: Jeffrey B. Parker and John A. Krommes
Abstract: In geophysical and plasma contexts, zonal flows are well known to arise
out of turbulence. We elucidate the transition from homogeneous turbulence without
zonal flows to inhomogeneous turbulence with steady zonal flows. Starting from
the equation for barotropic flow on a beta plane, we employ both the quasilinear
approximation and a statistical average, which retains a great deal of the qualitative
behavior of the full system. Within the resulting framework known as CE2, we
extend recent understanding of the symmetry-breaking zonostrophic instability and
show that it is an example of a Type Is instability within the pattern formation
literature. The broken symmetry is statistical homogeneity. Near the bifurcation
point, the slow dynamics of CE2 are governed by a well-known amplitude equation.
The important features of this amplitude equation, and therefore of the CE2 system,
are multiple. First, the zonal flow wavelength is not unique. In an idealized, infinite
system, there is a continuous band of zonal flow wavelengths that allow a nonlinear
equilibrium. Second, of these wavelengths, only those within a smaller subband are
stable. Unstable wavelengths must evolve to reach a stable wavelength; this process
manifests as merging jets. These behaviors are shown numerically to hold in the CE2
system. We also conclude that the stability of the equilibria near the bifurcation
point, which is governed by the Eckhaus instability, is independent of the Rayleigh-
Kuo criterion.
__________________________________________________
Submitted to: New Journal of Physics October 2013
__________________________________________________
Download PPPL-4958 (pdf 705 KB 30 pp)
__________________________________________________