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Distortions of inertia waves in a rotating fluid cylinder forced near its fundamental mode resonance

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 CB3 9EW, UK
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Abstract

A series of experimental observations is presented of a flow in which inertial oscillations are excited. The homogeneous fluid is contained in a completely filled right circular cylinder. The cylinder is spun about its axis of symmetry and a small ‘forced precession’ (or coning motion) is impulsively started. The flow is visualized by an electrolytic dyeline method. The mathematical problem for linear inviscid inertial oscillations in this system, although ill-posed in general, admits a solution in terms of wave modes for the specific boundary conditions considered here. The experiments show that while this linear inviscid theory provides some facility for predicting the flow structure at early times, the flow rapidly and irreversibly distorts away from the predicted form. This behaviour is seen as a precursor to some of the more dramatic breakdowns described by previous authors, and it may be pertinent to an understanding of the breakdowns reported in experiments on elliptical flow instabilities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 265 , 25 April 1994 , pp. 345 - 370
Copyright
© 1994 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
Baker, J. D. 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26, 573–575.Google Scholar
Fultz, D. 1959 A note on overstability, and the elastoid-inertia oscillations of Kelvin, Solberg and Bjerknes. J. Meteorol. 16, 199–208.Google Scholar
Gledzer, E. B., Dolzhanskii, F. V. & Obukhov, A. M. 1989 Instability of elliptical rotation and simple models of vortex fluid flows. Abstracts, Euromech 245: The effect of background rotation on fluid motions, Dept. Applied Math. & Theor. Physics, Cambridge, UK, April 10–13, 1989.
Gledzer, E. B. & Ponomarev, V. M. 1992 Instability of bounded flows with elliptical streamlines. J. Fluid Mech. 240, 1–30.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 non-uniformly rotating fluid. Phys. Fluids A 2, 2055–2060.Google Scholar
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
Kerswell, R. R. 1993 The instability of precessing flow. Geophys. Astrophys. Fluid Dyn. 72, 107–144.Google Scholar
Kudlick, M. D. 1966 On transient motions in a contained rotating fluid. PhD. thesis, Massachusetts Institute of Technology.
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
Malkus, W. V. R. & Waleffe, 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.
Manasseh, R. 1991 Inerita Wave breakdown: experiments in a precessing cylinder. PhD thesis, University of Cambridge.
Manasseh, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261–296.Google Scholar
Manasseh, R. 1993 Visualization of the flows in precessing tanks with internal baffles. Am. Inst. Aeronaut. Astronaut. J. 31, 312–318.Google Scholar
McEwan, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603–640.Google Scholar
McIntyre, M. E. & Norton, W. A. 1990 Dissipative wave-mean interactions and the transport of vorticity or potential vorticity. J. Fluid Mech. 212, 403–435.Google Scholar
Scott, P. R. & Tan, D. G. H. 1993 Complex-frequency method for computing the dynamics of liquid in a spinning container. J. Guidance, Control Dyn. 16, 190–196.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
Tan, D. G. H. 1991 Dynamics of a rotating body containing a liquid-filled cavity. Final Report (Volume 2). Dept. Applied Math. & Theor. Physics, University of Cambridge.
Thompson, R. 1970 Diurnal tides and shear instabilities in a rotating cylinder. J. Fluid Mech. 40, 737–751.Google Scholar
Waleffe, F. 1990 On the three dimensional instability of strained vortices. Phys. Fluids A 2, 76–80.Google Scholar
Wood, W. W. 1966 An oscillatory disturbance of rigidly rotating fluid. Proc. R. Soc. Lond. A 293, 181–212.Google Scholar