Dynamics of a 1-D model for the emergence of the plasma edge shear flow layer with momentum conserving Reynolds stress

TL;DR

This paper presents a 1-D model for plasma edge shear flow formation, incorporating momentum-conserving Reynolds stress, and analyzes its stability and stationary solutions, revealing connections to the Ginzburg-Landau equation.

Contribution

It introduces a momentum-conserving Reynolds stress model for plasma shear flows and analyzes its stability and stationary states.

Findings

Linear stability analysis performed.

Stationary solutions relate to the real Ginzburg-Landau equation.

Dynamics governed by a reduced shear flow equation.

Abstract

A one-dimensional version of the second-order transition model based on the sheared flow amplification by Reynolds stress and turbulence supression by shearing is presented. The model discussed in this paper includes a form of the Reynolds stress which explicitly conserves momentum. A linear stability analysis of the critical point is performed. Then, it is shown that the dynamics of weakly unstable states is determined by a reduced equation for the shear flow. In the case in which the flow damping term is diffusive, the stationary solutions are those of the real Ginzburg-Landau equation.