Statistical State Dynamics of Couette MHD Turbulence

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.