Passive scalar transport in Couette flow

Abstract

A scaling theory for the passive scalar transport in Couette flow, i.e. the flow between two parallel plates moving with different velocities, is proposed. This flow is determined by the bulk Reynolds number and the Prandtl number. In the turbulent regime, for moderate shear Reynolds number and moderate, we derive that the passive scalar transport characterised by the Nusselt number scales as. We then use the well-established scaling for the friction coefficient (corresponding to a shear Reynolds number) which holds reasonably well within the range, to obtain for the Nusselt number scaling. The theoretical results are tested against direct numerical simulations of Couette flows for the parameter ranges and, finding good agreement. Analyses of the numerically obtained turbulent flow fields confirm logarithmic mean wall-parallel profiles of the velocity and the passive scalar in the inertial sublayer.