A mixing-length model for side layers of magnetohydrodynamic channel and duct flows with insulating walls

Abstract

We propose a simple extension of Prandtl's classical mixing-length model for channel flow in order to describe the effects of a uniform spanwise magnetic field. The mixing length is assumed to be constrained by an additional length scale called the Joule damping length. It is based on the friction velocity and the Joule damping time. The limitation of mixing length is implemented by using the harmonic mean of the wall distance and the Joule damping length. Near the wall, the model captures the combined linear-logarithmic dependence of velocity on the wall distance observed in direct numerical simulations. It also provides a satisfactory prediction for the overall velocity distribution for different Reynolds and Hartmann numbers. The velocity profile of turbulent side layers in magnetohydrodynamic duct flows in a strong field can also be computed with the help of the model provided that the Hartmann layers are already laminar.