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On the initial-value problem in a rotating circular cylinder

Published online by Cambridge University Press:  08 August 2008

KEKE ZHANG  and
XINHAO LIAO
KEKE ZHANG
Affiliation:
Department of Mathematical Sciences, University of Exeter, Exeter, EX4 4QE, UK
XINHAO LIAO
Affiliation:
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
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Abstract

The initial-value problem in rapidly rotating circular cylinders is revisited. Four different but related analyses are carried out: (i) we derive a modified asymptotic expression for the viscous decay factors valid for the inertial modes of a broad range of frequencies that are required for an asymptotic solution of the initial value problem at an arbitrarily small but fixed Ekman number; (ii) we perform a fully numerical analysis to estimate the viscous decay factors, showing satisfactory quantitative agreement between the modified asymptotic expression and the fuller numerics; (iii) we derive a modified time-dependent asymptotic solution of the initial value problem valid for an arbitrarily small but fixed Ekman number and (iv) we perform fully numerical simulations for the initial value problem at a small Ekman number, showing satisfactory quantitative agreement between the modified time-dependent solution and the numerical simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 610 , 10 September 2008 , pp. 425 - 443
Copyright
Copyright © Cambridge University Press 2008

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References

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