Zonostrophic instability driven by discrete particle noise

TL;DR

This paper explores how discrete particle noise can induce a zonostrophic instability, leading to zonal flow formation in turbulence, without requiring intrinsic or extrinsic turbulence coupling, providing a new perspective on stochastic forcing.

Contribution

It introduces a novel interpretation of stochastic forcing in turbulence models as arising from particle noise, and analyzes the conditions for zonostrophic instability in a simplified plasma model.

Findings

Zonostrophic instability occurs just below linear instability threshold.

The instability point is independent of ion-ion collision rate.

A calculation of the neutral curve for a plasma model is provided.

Abstract

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just below the threshold for linear instability. The scenario provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic models such as the second-order cumulant expansion (CE2) or stochastic structural instability theory (SSST); neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To the extent that the damping of zonal flows is controlled by the ion--ion collision rate, the point of zonostrophic instability is independent of that rate.