TY - JOUR
T1 - Passive scalar transport in Couette flow
AU - Yerragolam, Guru Sreevanshu
AU - Stevens, Richard J.A.M.
AU - Verzicco, Roberto
AU - Lohse, Detlef
AU - Shishkina, Olga
N1 - Funding Information:
The authors gratefully acknowledge C. S. Ng and A. Blass for fruitful discussions. This work was financed from the ERC (European Research Council) starting grant No. 804283 UltimateRB. We acknowledge PRACE for awarding us access to MareNostrum at Barcelona Supercomputing Center (BSC), Spain (Project 2020235589 and 2020225335). The simulations were also supported by a grant from the Swiss National Supercomputing Center (CSCS) under project ID s997. We also acknowledge the Dutch national e-infrastructure of SURFsara, a subsidiary of SURF cooperation, the collaborative ICT organisation for Dutch education and research, the Twente Max-Planck Center and the Deutsche Forschungsgemeinschaft (DFG, SPP 1881 ‘Turbulent Superstructures’).
Publisher Copyright:
©
PY - 2022/7/25
Y1 - 2022/7/25
N2 - 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.
AB - 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.
KW - UT-Hybrid-D
U2 - 10.1017/jfm.2022.368
DO - 10.1017/jfm.2022.368
M3 - Article
SN - 0022-1120
VL - 943
SP - 1
EP - 21
JO - Journal of fluid mechanics
JF - Journal of fluid mechanics
M1 - A17
ER -