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Three-dimensional convection driven by centrifugal buoyancy

Published online by Cambridge University Press:  26 April 2006

M. Auer ,
F. H. Busse  and
R. M. Clever
M. Auer
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
F. H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
R. M. Clever
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
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Abstract

Convection driven by centrifugal buoyancy in a cylindrical fluid annulus cooled from the inside, heated from the outside, and rotating about its axis is described. While at high values of the dimensionless rotation parameter τ convection rolls aligned with the axis are preferred, three-dimensional patterns of convection are introduced at low values of τ through either the cross-roll instability or a subharmonic varicose instability. The instabilities are studied in terms of simple analytical relationships as well as through numerical methods based on the Galerkin scheme. Analytical expressions for the steady three-dimensional patterns induced by the instabilities are also derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 301 , 25 October 1995 , pp. 371 - 382
Copyright
© 1995 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
Busse, F. H. 1967 The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625–649.Google Scholar
Busse, F. H. 1971 Stability regions of cellular fluid flow. In Proc. IUTAM Symp. on Instability of Continuous Systems, Herrenalb, 1969 (ed. H. Leipholz), pp. 41–47. Springer.
Busse, F. H. 1976 A simple model of convection in the Jovian atmosphere. Icarus 20, 255–260.Google Scholar
Busse, F. H. 1983 Convection driven zonal flows in the major planets. Pageoph 121, 375–390.Google Scholar
Busse, F. H. 1988 Atmospheric dynamics of the major planets. In The Physics of the Planets (ed.) S. K. Runcorn), pp. 173–183. John Wiley & Sons.
Busse, F. H. 1994 Convection driven zonal flows and vortices in the major planets. Chaos 4, 123–134.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 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319–335.Google Scholar
Busse, F. H. & Clever, R. M. 1983 Stability of convection rolls in the presence of a horizontal magnetic field. J. Méc. Théor. Appl. 2, 495–502.Google Scholar
Busse, F. H. & Clever, R. M. 1989 Traveling wave convection in the presence of a horizontal magnetic field. Phys. Rev. A 40, 1954–1961.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
Busse, F. H. & Or, A. C. 1986 Convection in a rotating cylindrical annulus Part 1. Thermal Rossby waves. J. Fluid Mech. 166, 173–187.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Clever, R. M. & Busse, F. H. 1989 Three-dimensional knot convection in a layer heated from below. J. Fluid Mech. 198, 345–363.Google Scholar
Clever, R. M. & Busse, F. H. 1991 Instabilities of longitudinal rolls in the presence of Poiseuille flow. J. Fluid Mech. 229, 517–529.Google Scholar
Clever, R. M., Busse, F. H. & Kelly, R. E. 1977 Instabilities of longitudinal convection rolls in Couette flow. Z. Angew. Math. Phys. 28, 771–783.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.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar
Schnaubelt, M. & Busse, F. H. 1992 Convection in a rotating cylindrical annulus. Part 3. Vacillating and spatially modulated flow. J. Fluid Mech. 245, 155–173.Google Scholar