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On the viscous decay rates of inertial waves in a rotating circular cylinder

Published online by Cambridge University Press:  26 April 2006

R. R. Kerswell  and
C. F. Barenghi
R. R. Kerswell
Affiliation:
Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, UK
C. F. Barenghi
Affiliation:
Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, UK
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Abstract

In the literature, there are two different asymptotic results for the viscous decay rates of inertial modes in a rotating circular cylinder. In the absence of a viscous corner solution, either result can only be an estimate of the true decay rate. In this note, we numerically calculate the viscous decay rates for some experimentally excited inertial modes (Malkus 1989; Malkus & Waleffe 1991) in order to (i) assist in the interpretation of these experiments and (ii) to assess the usefulness of the two asymptotic estimates available. Our results indicate that the asymptotic estimate due to Kudlick (1966) is more accurate and that the asymptotic regime in which this estimate is useful (accurate to within 10%) can be smaller than is commonly thought.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 285 , 25 February 1995 , pp. 203 - 214
Copyright
© 1995 Cambridge University Press

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References

Aldridge, K. D. & Stergiopoulos, S. 1991 A technique for direct measurement of time-dependent complex eigenfrequencies of waves in fluids. Phys. Fluids A 3, 316–327.Google Scholar
Baines, P. G. 1967 Forced oscillations of an enclosed rotating fluid. J. Fluid Mech. 30, 533–546.Google Scholar
Bjerknes, V., Bjerknes, J., Solberg, H. & Bergeron, T. 1933 Physikalische Hydrodynamik, pp. 465–471. Springer.CrossRefGoogle Scholar
Fultz, D. 1959 A note on overstability, and the elastoid-inertia oscillations of Kelvin, Solberg and Bjerknes. J. Met. 16, 199–208.Google Scholar
Gans, R. F. 1970 On the precession of a resonant cylinder. J. Fluid Mech. 41, 865–872.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Hollerbach, R. 1994 Magnetohydrodynamic Ekman and Stewartson layers in a rotating spherical shell. Proc. R. Soc. Lond. A 444, 333–346.Google Scholar
Hollerbach, R. & Kerswell, R. R. 1994 Oscillatory, internal shear layers in rotating and precessing flows. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Johnson, L. E. 1967 The precessing cylinder. In Notes on the 1967 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Inst. Ref. 67–54, pp. 85–108.Google Scholar
Karpov, B. G. 1965 Dynamics of a liquid-filled shell: resonance and the effects of viscosity. BRL Rep. 1302. US Army Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland AD468654.Google Scholar
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.CrossRefGoogle Scholar
Kerswell, R. R. 1994a Tidal excitation of hydromagnetic waves and their damping in the Earth. J. Fluid Mech. 274, 219–241.Google Scholar
Kerswell, R. R. 1994b On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Kudlick, M. 1966 On the transient motions in a contained rotating fluid. PhD thesis, MIT.Google Scholar
Malkus, W. V. R. 1989 An experimental study of the global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder. Geophys. Astrophys. Fluid Dyn. 48, 123–134.Google Scholar
Malkus, W. V. R. & Walffe, F. A. 1991 Transition from order to disorder in elliptical flow: a direct path to shear flow turbulence. In Advances in Turbulence 3 (ed. A. V. Johansson & P. H. Alfredsson), pp. 197–203. Springer.CrossRefGoogle Scholar
Manasseh, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261–296.Google Scholar
Manasseh, R. 1994 Distortions of inertia waves in a rotating fluid cylinder forced near its fundamental mode resonance. J. Fluid Mech. 265, 345–370.Google Scholar
McEwan, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603–640.Google Scholar
Stergiopoulos, S. & Aldridge, K. D. 1982 Inertial waves in a fluid partially filling a cylindrical cavity during spin-up from rest. Geophys. Astrophys. Fluid Dyn. 21, 89–112.Google Scholar
Stergiopoulos, S. & Aldridge, K. D. 1987 Ringdown of inertial waves during spin-up from rest of a fluid contained in a rotating cylindrical cavity. Phys. Fluids 30, 302–311.Google Scholar
Stewartson, K. 1959 On the stability of a spinning top containing fluid. J. Fluid Mech. 5, 577–592.Google Scholar
Wedemeyer, E. H. 1966 Viscous corrections to Stewartson's stability criterion. BRL Rep. 1325. US Army Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland AD489687.Google Scholar
Whiting, R. D. & Gerber, N. 1980 Dynamics of liquid-filled gyroscope: update of theory and experiment. Rep. ARBRL-TR-02221. US Army Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland AD489687.Google Scholar
Wood, W. W. 1965 Properties of inviscid, recirculating flows. J. Fluid Mech. 22, 337–346.Google Scholar
Wood, W. W. 1966 An oscillatory disturbance of rigidly rotating fluid. Proc. R. Soc. Lond. A 293, 181–212.Google Scholar