Eur. Phys. J. B 26, 379-386 (2002)
https://doi.org/10.1140/epjb/e20020103

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

¹ CNRS, Groupe Instabilité et Turbulence, CEA/DRECAM/SPEC, 91191 Gif-sur-Yvette Cedex, France
² CNRS, Service d'Astrophysique, CE Saclay, 91191 Gif-sur-Yvette Cedex, France
³ CNRS, FRE2461, Laboratoire d'Études Spatiales et d'Instrumentation en Astrophysique, Observatoire de Meudon, 92195 Meudon Cedex, France

Corresponding author: ^a bdubru@discovery.saclay.cea.fr

Received: 7 June 2001
Revised: 7 December 2001
Published online: 15 April 2002

Abstract

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table [see full text]. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque , where L is the cylinder length, scales with Reynolds number R and gap width η, . At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: These predictions are found to be in excellent agreement with avail- able experimental data. Predictions for scaling of velocity fluctuations are also provided.