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Oscillatory internal shear layers in rotating and precessing flows

Published online by Cambridge University Press:  26 April 2006

R. Hollerbach  and
R. R. Kerswell
R. Hollerbach
Affiliation:
Institute of Geophysics and Planetary Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
R. R. Kerswell
Affiliation:
Department of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK
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Abstract

We present a direct numerical solution of a particular inertial oscillation, the so-called 'spin-over’ mode, in spherical geometry. This mode is particularly relevant to the fluid flow within a precessing oblate spheroid. We demonstrate that the oscillatory Ekman layer breaks down at ±30° latitude, and that this breakdown spawns internal shear layers. We show that the structure of these shear layers is different for a full sphere and a spherical shell, as noted in the preceding paper (Kerswell 1995). Despite the existence of these shear layers, however, the numerical decay rates agree to within 1 % with the asymptotic decay rates, which neglect any possible shear layers. Finally, we consider the nonlinear mean flow profiles driven by this mode, and demonstrate that our numerical results agree reasonably well with experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 327 - 339
Copyright
© 1995 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1968 Handbook of Mathematical Functions. Dover.
Aldridge, K. D. 1972 Axisymmetric inertial oscillations of a fluid in a rotating spherical shell. Mathematika 19, 163–168.Google Scholar
Aldridge, K. D. & Toomre, A. 1969 Axisymmetric inertial oscillations of a fluid in a rotating spherical container. J. Fluid Mech. 37, 307–323.Google Scholar
Busse, F. H. 1968 Steady fluid flow in a precessing spheroidal shell. J. Fluid Mech. 33, 739–751.Google Scholar
Fearn, D. R. 1991 Eigensolutions of boundary value problems using inverse iteration. J. Comput. Appl. Math. 34, 201–209.Google Scholar
Greenspan, H. P. 1964 On the transient motion of a contained rotating fluid. J. Fluid Mech. 21, 673–696.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hollerbach, R. 1994a Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell. Phys. Fluids 6, 2540–2544.Google Scholar
Hollerbach, R. 1994b Magnetohydrodynamic Ekman and Stewartson layers in a rotating spherical shell. Proc. R. Soc. Lond. A 444, 333–346.Google Scholar
Kerswell, R. R. 1993 The instability of prcessing flow. Geophys. Astrophys. Fluid Dyn. 72, 107–144.Google Scholar
Kerswell, R. R. 1995 On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers. J. Fluid Mech. 298 311–325 (referred to herein as I).Google Scholar
Malkus, W. V. R. 1968 Precession of the Earth as the cause of geomagnetism. Science 169, 259–264.Google Scholar
Peters, G. & Wilkinson, J. H. 1971 The calculation of specified eigenvectors by inverse iteration. Handbook for Automatic Computation Vol. 2, pp. 418–439. Springer.
Poincaré, H. 1910 Sur la précession des corps déformables. Bull. Astron. 27, 321–356.Google Scholar
Roberts, P. H. & Stewartson, K. 1963 On the stability of a Maclaurin spheroid of small viscosity. Astrophys. J. 137, 777–790.Google Scholar
Stewartson, K. & Roberts, P. H. 1963 On the motion of a liquid in a spheroidal cavity of a precessing rigid body. J. Fluid Mech. 17, 1–20.Google Scholar
Vanyo, J. P., Wilde, P., Cardin, P. & Oolson, P. 1995 Experiments on precessing flows in the Earth's liquid core. Geophys. J. Intl 121, 136–142.Google Scholar
Walton, I. C. 1975 Viscous shear layers in an oscillating rotating fluid. Proc. R. Soc. Lond. A 344, 101–110.Google Scholar