A nonlinear approach to transition in subcritical plasmas with sheared flow

TL;DR

This paper investigates the nonlinear transition to turbulence in subcritical plasmas with sheared flow, using advanced methods to identify the minimal disturbances needed to trigger turbulence and the structure of the transition boundary.

Contribution

It introduces two nonlinear analysis methods—edge tracking and nonlinear non-modal stability theory—to characterize transition mechanisms in sheared plasma flows, revealing the structure of the transition boundary.

Findings

Edge is structured around a localized traveling wave solution.

Identified the minimal seed for turbulence triggering.

Provided a semi-analytic approximation for the minimal seed.

Abstract

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution; a solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provides confidence in the derivation of a semi-analytic approximation for the minimal seed.