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Thermal instabilities in rapidly rotating systems

  • F. H. Busse (a1)

Thermal instabilities of a contained fluid are investigated for a fairly general class of problems in which the dynamics are dominated by the effects of rotation. In systems of constant depth in the direction of the axis of rotation the instability develops when the buoyancy forces suffice to overcome the stabilizing effects of thermal conduction and of viscous dissipation in the Ekman boundary layers. Owing to the Taylor–Proudman theorem, a slight gradient in depth exerts a strongly stabilizing influence. The theory is applied to describe the instability of the ‘lower symmetric régime’ in the rotating annulus experiments at high rotation rates. An example of geophysical relevance is the instability of a self-gravitating, internally heated, rotating fluid sphere. The results of the perturbation theory for this problem agree reasonably well with the results of an extension of the analysis by Roberts (1968).

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Bisshopp, F. E. & Niller, P. P. 1965 J. Fluid Mech. 23, 45.
Busse, F. H. 1968 J. Fluid Mech. 33, 57.
Busse, F. H. 1970 Astrophys. J. 159, 62.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon.
Fowlis, W. W. & Hide, R. 1965 J. Atmos. Sci. 22, 54.
Fultz, O. 1961 Adv. Geophysics, 7, 1.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hide, R. 1958 Phil. Trans. A 250, 441.
Hunter, C. 1967 J. Fluid Mech. 27, 75.
Roberts, P. H. 1965 Astrophys. J. 141, 24.
Roberts, P. H. 1968 Phil. Trans. A 263, 93.
Robinson, A. R. 1959 J. Fluid Mech. 6, 59.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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