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A rotating fluid cylinder subject to weak precession

Published online by Cambridge University Press:  06 March 2008

PATRICE MEUNIER ,
CHRISTOPHE ELOY ,
ROMAIN LAGRANGE  and
FRANÇOIS NADAL
PATRICE MEUNIER
Affiliation:
IRPHE, CNRS, Universités Aix Marseille I & II, 49 rue Joliot–Curie, 13013 Marseille, France
CHRISTOPHE ELOY
Affiliation:
IRPHE, CNRS, Universités Aix Marseille I & II, 49 rue Joliot–Curie, 13013 Marseille, France
ROMAIN LAGRANGE
Affiliation:
IRPHE, CNRS, Universités Aix Marseille I & II, 49 rue Joliot–Curie, 13013 Marseille, France
FRANÇOIS NADAL
Affiliation:
Commissariat à l'Energie Atomique, CESTA, 33114 le Barp, France
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Abstract

In this paper, we report experimental and theoretical results on the flow inside a precessing and rotating cylinder. Particle image velocimetry measurements have revealed the instantaneous structure of the flow and confirmed that it is the sum of forced inertial (Kelvin) modes, as predicted by the classical linear inviscid theory. But this theory predicts also that the amplitude of a mode diverges when its natural frequency equals the precession frequency. A viscous and weakly nonlinear theory has therefore been developed at the resonance. This theory has been compared to experimental results and shows a good quantitative agreement. For low Reynolds numbers, the mode amplitude scales as the square root of the Reynolds number owing to the presence of Ekman layers on the cylinder walls. When the Reynolds number is increased, the amplitude saturates at a value which scales as the precession angle to the power one-third for a given resonance. The nonlinear theory also predicts the forcing of a geostrophic (axisymmetric) mode which has been observed and measured in the experiments. These results allow the flow inside a precessing cylinder to be fully characterized in all regimes as long as there is no instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 405 - 440
Copyright
Copyright © Cambridge University Press 2008

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