Passive scalar transport in Couette flow

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 Re-b and the Prandtl number Pr. In the turbulent regime, for moderate shear Reynolds number Re-tau and moderate Pr, we derive that the passive scalar transport characterised by the Nusselt number Nu scales as Nu similar to (PrRe tau Reb-1)-Re-1/-Re-2-Re-2. We then use the well-established scaling for the friction coefficient C-f similar to Re-b(-1/4) (corresponding to a shear Reynolds number Re-tau similar to Re-b(7/)8) which holds reasonably well within the range 3 x 10(3) <= Re-b <= 10(5), to obtain Nu similar to pr(1/2)Re(b)(3/4) for the Nusselt number scaling. The theoretical results are tested against direct numerical simulations of Couette flows for the parameter ranges 81 <= Re-b <= 22361 and 0.1 <= Pr <= 10, 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.