Self-organization through layering of β-plane-like turbulence in plasmas and geophysical fluids

Abstract

Staircase formation and layering is studied in simplified, potential vorticity (PV) conserving models of plasmas and geophysical fluids, by investigating turbulent self-organization and nonlinear saturation with different mechanisms of free energy production—forcing or linear instability—and with standard or modified zonal flow (ZF) responses. To this end, staircase formation in both the standard and modified Charney–Hasegawa–Mima (CHM) equations with stochastic forcing, along with two different simple instability-driven models—one from a plasma and one from a geophysical context—are studied and compared. In these studies, it is observed that β-plane turbulence that does not distinguish between zonal and non-zonal perturbations (i.e. standard zonal response) gradually forms large-scale, elliptic zonal structures that merge progressively, regardless of whether it is driven by forcing (though it should be weak and slow enough to allow wave couplings) or by baroclinic instability, using, for example, a two-layer model. Conversely, the plasma system, with its modified zonal response, can rapidly form straight, stationary jets of well-defined size, again regardless of the way it is driven: by stochastic forcing or by the dissipative drift-wave instability. Furthermore, the instability-driven plasma system exhibits a subcritical zonal bifurcation, which resembles a phase transition, between a ZF dominated state and an eddy dominated state. In both states, saturation is possible without large-scale friction.

This article is part of the theme issue ‘Anti-diffusive transport and layering: from sub-cellular to astrophysical scales’.