Ensemble-mean modeling of two-equation type in magnetohydrodynamic turbulent shear flows

Ensemble-mean two-equation modeling is studied in magnetohydrodynamic turbulent shear flows. This model consists of a system of equations governing the mean velocity, the mean magnetic field, the total turbulent energy (the sum of turbulent kinetic and magnetic energy), and its dissipation rate. The turbulence effect in the Navier--Stokes equation is written in the form of an eddy-viscosity representation, whereas the counterpart in the mean magnetic induction equation is expressed in the combination of alpha dynamo terms and an eddy-magnetic diffusivity representation. The implication of the present model in reversed-field pinches of plasma in controlled nuclear fusion is also discussed