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_τ and moderate Pr, we derive that the passive scalar transport characterised by the Nusselt number Nu scales as Nu ∼ Pr^1/2Re² _τRe_b⁻¹. We then use the well-established scaling for the friction coefficient Cf ∼ Re_b^−1/4 (corresponding to a shear Reynolds number Re_τ ∼ Re_b^7/8) which holds reasonably well within the range 3 × 10³ ≤ Re_b ≤10⁵, to obtain Nu ∼ Pr^1/2Re_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. [ABSTRACT FROM AUTHOR]