Passive scalar transport in Couette flow

Guru Sreevanshu Yerragolam*, Richard J.A.M. Stevens, Roberto Verzicco, Detlef Lohse*, Olga Shishkina

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 Reb and the Prandtl number Pr. In the turbulent regime, for moderate shear Reynolds number Reτ and moderate Pr, we derive that the passive scalar transport characterised by the Nusselt number Nu scales as Nu∼Pr1/2Re2τRe−1b. We then use the well-established scaling for the friction coefficient Cf∼Re−1/4b (corresponding to a shear Reynolds number Reτ∼Re7/8b) which holds reasonably well within the range 3×103⩽Reb⩽105, to obtain Nu∼Pr1/2Re3/4b for the Nusselt number scaling. The theoretical results are tested against direct numerical simulations of Couette flows for the parameter ranges 81⩽Reb⩽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.
Original languageEnglish
Article numberA17
Pages (from-to)1-21
Number of pages21
JournalJournal of fluid mechanics
Early online date9 Jun 2022
Publication statusPublished - 25 Jul 2022


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