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Abstract:
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.
