TY - JOUR
T1 - Calculation of the mean velocity profile for strongly turbulent Taylor-Couette flow at arbitrary radius ratios
AU - Berghout, Pieter
AU - Verzicco, Roberto
AU - Stevens, Richard J.A.M.
AU - Lohse, Detlef
AU - Chung, Daniel
N1 - Cambridge UP deal
PY - 2020/12/25
Y1 - 2020/12/25
N2 - Taylor-Couette (TC) flow is the shear-driven flow between two coaxial independently rotating cylinders. In recent years, high-fidelity simulations and experiments revealed the shape of the streamwise and angular velocity profiles up to very high Reynolds numbers. However, due to curvature effects, so far no theory has been able to correctly describe the turbulent streamwise velocity profile for a given radius ratio, as the classical Prandtl-von Kármán logarithmic law for turbulent boundary layers over a flat surface at most fits in a limited spatial region. Here, we address this deficiency by applying the idea of a Monin-Obukhov curvature length to turbulent TC flow. This length separates the flow regions where the production of turbulent kinetic energy is governed by pure shear from that where it acts in combination with the curvature of the streamlines. We demonstrate that for all Reynolds numbers and radius ratios, the mean streamwise and angular velocity profiles collapse according to this separation. We then develop the functional form of the velocity profile. Finally, using the newly developed angular velocity profiles, we show that these lead to an alternative constant in the model proposed by Cheng et al. (J. Fluid Mech., vol. 890, 2020, A17) for the dependence of the torque on the Reynolds number, or, in other words, of the generalized Nusselt number (i.e. the dimensionless angular velocity transport) on the Taylor number.
AB - Taylor-Couette (TC) flow is the shear-driven flow between two coaxial independently rotating cylinders. In recent years, high-fidelity simulations and experiments revealed the shape of the streamwise and angular velocity profiles up to very high Reynolds numbers. However, due to curvature effects, so far no theory has been able to correctly describe the turbulent streamwise velocity profile for a given radius ratio, as the classical Prandtl-von Kármán logarithmic law for turbulent boundary layers over a flat surface at most fits in a limited spatial region. Here, we address this deficiency by applying the idea of a Monin-Obukhov curvature length to turbulent TC flow. This length separates the flow regions where the production of turbulent kinetic energy is governed by pure shear from that where it acts in combination with the curvature of the streamlines. We demonstrate that for all Reynolds numbers and radius ratios, the mean streamwise and angular velocity profiles collapse according to this separation. We then develop the functional form of the velocity profile. Finally, using the newly developed angular velocity profiles, we show that these lead to an alternative constant in the model proposed by Cheng et al. (J. Fluid Mech., vol. 890, 2020, A17) for the dependence of the torque on the Reynolds number, or, in other words, of the generalized Nusselt number (i.e. the dimensionless angular velocity transport) on the Taylor number.
KW - UT-Hybrid-D
KW - Taylor-Couette flow
KW - turbulent boundary layers
KW - stratified turbulence
UR - http://www.scopus.com/inward/record.url?scp=85095450709&partnerID=8YFLogxK
U2 - 10.1017/jfm.2020.739
DO - 10.1017/jfm.2020.739
M3 - Article
AN - SCOPUS:85095450709
SN - 0022-1120
VL - 905
JO - Journal of fluid mechanics
JF - Journal of fluid mechanics
M1 - A11
ER -