Zonal Flow as Pattern Formation

TL;DR

This paper demonstrates that steady-state zonal flows and turbulence in a generalized Hasegawa-Mima model can be understood as pattern formation, revealing multiple possible wavelengths and stability properties.

Contribution

It introduces a pattern formation framework for zonal flows in a stochastic turbulence model, highlighting wavelength multiplicity and stability criteria.

Findings

Multiple steady-state wavelengths exist within a continuous band.

Only a subset of wavelengths are linearly stable.

Unstable wavelengths evolve through jet merging.

Abstract

Zonal flows are well known to arise spontaneously out of turbulence. We show that for statistically averaged equations of the stochastically forced generalized Hasegawa-Mima model, steady-state zonal flows and inhomogeneous turbulence fit into the framework of pattern formation. There are many implications. First, the wavelength of the zonal flows is not unique. Indeed, in an idealized, infinite system, any wavelength within a certain continuous band corresponds to a solution. Second, of these wavelengths, only those within a smaller subband are linearly stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets.