Quasilinear theory of hydrodynamic turbulence and instability of plane-parallel plasma flows

V. I. Aref'ev

Abstract
A study is made of the stability of a plane-parallel flow of conducting fluid between parallel plates. A method of finding the approximate eigenvalues of the boundary-value problem is proposed by means of which it is possible to find the boundary of unstable oscillations in the quasilinear approximation, when the flow profile, as a result of the establishment of a quasiequilibrium level of turbulence from an unstable laminar flow, becomes a stable turbulent profile. The equation determining the stability boundary describes the profile of the steady turbulent flow. The velocity and magnetic field profiles of a turbulent MHD flow are investigated in the quasilinear approximation; the characteristic effect of layering of the flow that is observed experimentally is demonstrated.