Statistical State Dynamics based Theory for Couette MHD Turbulence and Dynamo Formation

The roll–streak structure (RSS) is ubiquitous in wall-bounded shear flow turbulence (Kline et al. 1962; Smith & Metzler 1983) and also appears in magnetized plasmas (Jones & Palmer 1965). Previous studies employing Statistical State Dynamics (SSD) analyzed the mechanism underlying RSS formation in shear flows (Farrell & Ioannou 2012; Farrell et al. 2016), revealing a mechanism by which background turbulence can destabilize the classical lift-up process, resulting in emergence of perturbation instabilities with RSS form leading to finite amplitude fixed point and self-sustaining turbulent RSS.  Remarkably, the structure of the ω-dynamo growth mechanism is mathematically analogous to this mechanism, differing primarily by a sign reversal in the shear term. This parallellism suggests that background turbulence in MHD flows may similarly destabilize the ω-dynamo mechanism. While conventional α–ω dynamo theory introduces field regeneration through an ad hoc scalar α parameter to represent the conversion from toroidal to poloidal field components, it does not derive this conversion from the full induction dynamics. Here, we develop a new SSD-based theoretical framework that self-consistently captures the coupled formation and maintenance of both velocity-field RSS and magnetic-field dynamo action within Couette MHD turbulence.