Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-08T05:38:42.317Z Has data issue: false hasContentIssue false
  • English
  • Français

Azimuthal flow associated with inertial wave resonance in a precessing cylinder

Published online by Cambridge University Press:  26 April 2006

J. Jonathan Kobine
J. Jonathan Kobine
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK Present address: Department of Atmospheric Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

A series of experiments has been carried out on low-viscosity fluid in a right-circular cylinder that rotates rapidly at a constant speed about its axis of symmetry. This axis in turn is made to undergo less rapid precession about a second axis passing through the centroid of the cylinder. The linear inviscid response of the fluid to such forcing can be expressed as a spectrum of inertial wave modes. However, there are several interesting features of the problem that are associated with nonlinear and viscous effects. One such phenomenon is the appearance of an azimuthal flow under conditions that are related to the underlying linear inertial wave behaviour. Results are presented concerning the manner in which this flow depends on the various experimental parameters. Dynamical properties of the circulation following the onset of forcing have also been investigated. The flow at forcing frequencies close to the fundamental inertial wave resonance was found to have a vortex-like structure, and this led to data that suggest that hydrodynamic instabilities may play a part in the observed breakdown to turbulent motion in regimes of strong forcing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 319 , 25 July 1996 , pp. 387 - 406
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Busse, F. H. 1968 Steady fluid flow in a precessing spheroidal shell. J. Fluid Mech. 33, 739–751.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Fultz, D. 1959 A note on the overstability of the elastoid-inertia oscillations of Kelvin, Solberg and Bjerknes. J. Met. 16, 199–208.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Gunn, J. S. & Aldridge, K. D. 1990 Inertial wave eigenfrequencies for a nonuniformly rotating fluid. Phys. Fluids A 2, 2055–2060.Google Scholar
Hall, P., Sedney, R. & Gerber, N. 1992 High Reynolds number flows in rotating and nutating cylinders: spatial eigenvalue approach. AIAA J. 30, 423–430.Google Scholar
Herbert, T. 1986 Viscous fluid motion in a spinning and nutating cylinder. J. Fluid Mech. 167, 181–198.Google Scholar
Hollerbach, R. & Kerswell, R. R. 1995 Oscillatory internal shear layers in rotating and processing flows. J. Fluid Mech. 298, 327–339.Google Scholar
Johnson, L. E. 1967 The precessing cylinder. In Notes on the 1967 Summer Study Programme in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Inst., vol. 2, pp. 85–108.Google Scholar
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.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.Google Scholar
Kobine, J. J. 1995 Inertial wave dynamics in a rotating and precessing cylinder. J. Fluid Mech. 303, 233–252.Google 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
Pocha, J. J. 1987 An experimental investigation of spacecraft sloshing. Space Commun. Broadcasting 5, 323–332.Google Scholar
Roberts, P. H. & Stewartson, K. 1965 On the motion of a liquid in a spheroidal cavity of a precessing rigid body. II. Proc. Camb. Phil. Soc. 61, 279–288.Google Scholar
Selmi, M. & Herbert, T. 1995 Resonance phenomena in viscous fluids inside partially filled spinning and nutating cylinders. Phys. Fluids 7, 108–120.Google Scholar
Selmi, M., Li, R. & Herbert, T. 1992 Eigenfunction expansion of the flow in a spinning and nutating cylinder. Phys. Fluids A 4, 1998–2007.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
Thompson, R. 1970 Diurnal tides and shear instabilities in a rotating cylinder. J. Fluid Mech. 40, 737–751.Google Scholar
Vanyo, J., Wilde, P., Cardin, P. & Olson, P. 1995 Experiments on precessing flows in the Earth's liquid core. Geophys. J. Intl 121, 136–142.Google Scholar
Vaughn, H. R., Oberkampf, W. L. & Wolfe, W. P. 1985 Fluid motion inside a spinning nutating cylinder. J. Fluid Mech. 150, 121–138.Google Scholar