Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-04T21:07:59.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Breakdown regimes of inertia waves in a precessing cylinder

Published online by Cambridge University Press:  26 April 2006

Richard Manasseh
Richard Manasseh
Affiliation:
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB2 9EW, UK School of Mathematics, Oceanography Group, University of New South Wales, PO Box 1, Kensington, NSW 2033, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

A series of experimental studies have been made of the fluid behaviour in a completely filled, precessing, right circular cylinder. The tank was spun about its axis of symmetry and subjected to a forced precession at various excitation frequencies ω, nutation angles θ and at various Ekman numbers. This forcing excites a subset of the modes, called inertia waves, that are made possible by the Coriolis force that arises in a spinning environment. In these experiments, the fluid flow breakdown phenomena are investigated. Here the fluid, when forced near a resonant frequency, exhibits a transition to disordered or turbulent flow. This paper presents a categorization of some of the breakdown regimes, of which the ‘resonant collapses’ (McEwan 1970) are the most catastrophic members.

The studies reported in this paper used entirely visual observations and measurements. The experimental observations employed a visualization technique that gave no information on fluid velocities, but provided an excellent picture of the flow structure. Quantitative data were extracted in the form of the time for the breakdown to occur. The breakdown phenomena, while readily produced over a large region of parameter space, are complex and varied. The observations show that our system is extraordinarily rich, exhibiting, for example, recurrent breakdowns which may be explained in terms of chaotic intermittency. A detailed description of some of the different breakdown regimes indicates that no single model will explain the behaviour throughout parameter space. This research is motivated by the instability problems of spinning spacecraft containing liquid fuels.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 261 - 296
Copyright
© 1992 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

Baines, P. G. 1967 Forced oscillations of an enclosed rotating fluid. J. Fluid Mech. 30, 533–546.Google 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
Gledzer, Ye. B., Dolzhanskii, F. V. & Oboukhov, A. M. 1989 Instability of elliptical rotation and simple models of vortex fluid shows. Abstracts, Euromech 245: The Effect of Background Rotation on Fluid Motions, Department of Applied Mathematics and Theoretical Physics, Cambridge, UK, April 10–13 1989.
Gledzer, Ye. B., Kovikov, Yu. V., Oboukhov, A. M. & Chusov, M. A. 1974 An investigation of the stability of liquid flows in a three-axis ellipsoid. Izv. Acad. Sci. USSR Atmos. Ocean Phys. Bull. 10 (2), 115–118.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Griffiths, R. W. & Linden, P. F. 1985 Intermittent baroclinic instability and fluctuations in geophysical contexts. Nature 316, 801–803.Google Scholar
Gunn, J. S. & Aldridge, K. D. 1990 Inertial wave eigenfrequencies for a non-uniformly rotating fluid.. Phys. Fluids A 2, 2055–2060.Google 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.
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
Kudlick, M. 1966 On transient motions in a contained rotating fluid. Ph.D. thesis. Massachusetts Institute of Technology, February 1966.
Malkus, W. V. R. 1968 Precession of the Earth as the cause of geomagnetism. Science 160, 259–264.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
Manasseh, R. 1991 Inertia wave breakdown: experiments in a precessing cylinder. Ph.D. thesis, University of Cambridge.
Mcewan, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603–640.Google Scholar
Mcewan, A. D. 1971 Degeneration of resonantly-excited standing internal gravity waves. J. Fluid Mech. 50, 431–448.Google Scholar
Mcewan, A. D. 1983 Internal mixing in stratified fluids. J. Fluid Mech. 128, 59–80.Google Scholar
Mcewan, A. D., Mander, D. W. & Smith, R. K. 1972 Forced resonant second-order interaction between damped internal waves. J. Fluid Mech. 55, 589–608.Google Scholar
Savasl, ö. 1985 On flow visualisation using reflective flakes. J. Fluid Mech. 152, 235–248.Google Scholar
Scott, W. E. 1975 The frequency of inertial waves in a rotating, sectored cylinder. J. Appl. Mech. Trans. ASME E: 43, 571–574.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
Suess, S. T. 1971 Viscous flow in a deformable rotating container. J. Fluid Mech. 45, 189–201.Google Scholar
Thompson, R. 1970 Diurnal tides and shear instabilities in a rotating cylinder. J. Fluid Mech. 40, 737–751.Google Scholar
Waleffe, F. 1988 3D Instability of bounded elliptical flow. (M.I.T.) Woods Hole GFD Fellow Report, August 1988.
Whiting, R. D. 1981 An experimental study of forced asymmetric oscillations in a rotating liquid filled cylinder. Ballistic Research Labs. Rep. ARBRL-TR-02376.
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