Statistical State Dynamics of Couette MHD Turbulence

TL;DR

This paper demonstrates that the roll streak structure in wall-bounded shear flow MHD turbulence arises from an instability in the statistical state dynamics, leading to self-sustaining turbulent states and large-scale dynamos.

Contribution

It extends the concept of statistical state dynamics to MHD turbulence, providing an analytic solution for the velocity-magnetic field structure and identifying the instability mechanisms involved.

Findings

Identifies an instability leading to the formation of the RSS in MHD SSD.

Shows that the system can reach fixed points or turbulent states.

Demonstrates the existence of large-scale coherent dynamos in these states.

Abstract

The roll streak structure (RSS) is ubiquitous in shear flow turbulence and is fundamental to the dynamics of the self-sustaining process (SSP) maintaining the turbulent state. The formation and maintenance of the RSS in wall-bounded shear flow suggest the presence of an underlying instability that has recently been identified using statistical state dynamics (SSD). Due to the parallelism between the Navier-Stokes equation and the induction equation, it is reasonable to inquire whether the RSS in wall-bounded shear flow has a counterpart in the MHD equations formulated as an SSD. In this work we show that this is the case and that an analytic solution for the composite velocitymagnetic field RSS in the MHD SSD also arises from an instability, that this instability equilibrates to either a fixed point or to a turbulent state, that these turbulent statistical equilibria may be self sustaining, and that both the fixed point and the turbulent states may correspond to large scale coherent dynamos.