135.
We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. 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
G =
T/ν
2
L, where
L is the cylinder length, scales with Reynolds number
R and gap width η,
G = 1.46η
3/2(1 - η)
-7/4
R
3/2. 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:
G = 0.50
. These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity
fluctuations are also provided.
Received 7 June 2001 and Received in final form 7 December 2001
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