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Convection in a rotating cylindrical annulus Part 3. Vacillating and spatially modulated flows

Published online by Cambridge University Press:  26 April 2006

M. Schnaubelt  and
F. H. Busse
M. Schnaubelt
Affiliation:
Institute of Physics, University of Bayreuth, D-8580 Bayreuth. Germany
F. H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, D-8580 Bayreuth. Germany
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Abstract

The problem of convection driven by radial buoyancy in a rotating cylindrical annulus with conical end surfaces represents one of the basic models of rotating fluid dynamics with applications to convection in planets and stars. Although only two-dimensional equations govern the flow in the limit of high rotation rates, a surprising variety of different states of motion can be found. In this paper earlier numerical work is extended by the consideration of rigid boundary conditions at the cylindrical walls and by a study of spatially modulated convection. Of particular interest is the case of curved conical end surfaces which appears to promote the formation of separate cylindrical convection layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 155 - 173
Copyright
© 1992 Cambridge University Press

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References

Azouni A., Bolton, E. W. & Busse F. H. 1986 Experimental study of convection columns in a rotating cylindrical annulus. Geophys. Astrophys. Fluid Dyn. 34, 301–317.Google Scholar
Brummell, N. H. & Hart J. E. 1992 High Rayleigh number -convection. Geophys. Astrophys. Fluid Dyn. (in press).Google Scholar
Busse F. H. 1970 Thermal instabilities in rapidly rotating system. J. Fluid Mech. 44, 441–460.Google Scholar
Busse F. H. 1976 A simple model of convection in the Jovian atmosphere. Icarus 20, 255–260.Google Scholar
Busse F. H. 1982 Thermal convection in rotating systems. In Proc. Ninth US Natl Congr. of Applied Mechanics, pp. 299–305. ASME.
Busse F. H. 1983 A model of mean zonal flow in the major planets. Geophys. Astrophys. Fluid Dyn. 23, 153–174.Google Scholar
Busse F. H. 1984 Transition to turbulence via the statistical limit cycle route. In Turbulence and Chaotic Phenomena in Fluids (ed. by T. Tatsumi), pp. 197–202. Elsevier.
Busse F. H. 1986 Asymptotic theory of convection in a rotating, cylindrical annulus. J. Fluid Mech. 173, 545–556.Google Scholar
Busse, F. H. & Carrigan C. R. 1974 Convection induced by centrifugal buoyancy. J. Fluid Mech. 62, 579–592.Google Scholar
Busse, F. H. & Clever R. M. 1979 Nonstationary convection in a rotating system. In Recent Developments in Theoretical and Experimental Fluid Mechanics (ed. U. Müller, K. G. Roesner & B. Schmidt), pp. 376–385. Springer.
Busse, F. H. & Heikes K. E. 1980 Convection in a rotating layer: A simple case of turbulence. Science 208, 173–175.Google Scholar
Busse, F. H. & Hood L. L. 1982 Differential rotation driven by convection in a rotating annulus. Geophys. Astrophys. Fluid Dyn. 21, 59–74.Google Scholar
Chandrasekhar S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Hide, R. & Mason P. J. 1975 Sloping convection in a rotating fluid. Adv. Phys. 24, 47–100.Google Scholar
Küppers, G. & Lortz D. 1969 Transition from laminar convection to thermal turbulence in a rotating fluid layer. J. Fluid Mech. 35, 609–620.Google Scholar
Or A. C. 1990 New phenomena in the Eckhaus instability of thermal Rossby waves. J. Fluid Mech. 216, 613–628.Google Scholar
Or, A. C. & Busse F. H. 1987 Convection in a rotating cylindrical annulus. Part 2. Transitions to asymmetric and vacillating flow. J. Fluid Mech. 174, 313–326 (referred to herein as OB87).Google Scholar
Schnaubelt M. 1992 Stationäre und zeitabhängige Konvektion im rotierenden zylindrischen Annulus. dissertation, University of Bayreuth.
Schnaubelt, M. & Busse F. H. 1990 Convection in a rotating cylindrical annulus with rigid boundaries. In Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems (ed. F. H. Busse & L. Kramer), pp. 67–72. Plenum NATO Series.