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On rotating thermal convection driven by non-uniform heating from below

Published online by Cambridge University Press:  20 April 2006

Phillip Hignett ,
Alan Ibbetson  and
Peter D. Killworth
Phillip Hignett
Affiliation:
Meteorological Office, Bracknell, Berkshire
Alan Ibbetson
Affiliation:
Department of Meteorology, University of Reading
Peter D. Killworth
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Experiments are described in which a radial temperature gradient is maintained along the lower horizontal boundary of a rotating annulus containing a thermally convecting fluid; the vertical side walls and upper horizontal boundary are nominally insulating. Comparison is made with the non-rotating experiments of Rossby (1965) and the same general asymmetric circulation is observed, i.e. that of a weakly stratified interior of slowly descending fluid occupying most of the annular gap, overlying a thin thermal layer of large vertical temperature gradients, stable over the cold part of the base and statically unstable over the warmer part; the circulation is completed by a narrow region of rising motion at the warm end of the base.

A boundary-layer scaling analysis demonstrates the existence of six flow regimes, depending on the magnitude of a quantity Q defined such that Q is the square of the ratio of the (non-rotating) thermal-layer scale to the Ekman-layer scale. For small Q the flow is only weakly modified by rotation but as Q increases past unity rotation tends to thicken the thermal layer. Also presented are some numerical similarity solutions for the special case of a quadratic temperature distribution on the lower boundary and partially covering the range of Q achieved in the experiments, which is zero to ten. Above a certain critical value of Q (for the geometry used here Qc = 3·4) a baroclinic wave regime exists but is not examined in detail here although a brief discussion of an instability problem is given. Throughout comparisons are drawn between the experimental results and theoretical aspects of the problem.

It is thought that the essential features of a system thermally driven in this way have their counterparts in natural systems such as the large-scale thermally induced ocean circulation driven by the latitudinal variation of incoming solar radiation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 161 - 187
Copyright
© 1981 Cambridge University Press

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References

Baker, D. J. 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26, 573–575.Google Scholar
Barcilon, V. 1964 Role of Ekman layers in the stability of the symmetric regime obtained in a rotating annulus. J. Atmos. Sci. 21, 291–299.Google Scholar
Beardsley, R. C. & Festa, J. F. 1972 A numerical model of convection driven by a surface stress and non-uniform heating. J. Phys. Oceanogr. 2, 444–455.Google Scholar
Bjerknes, V. 1916 Leipzig, Abh. Ges. Wins. 35, 29.
Daniels, P. G. 1976 Thermal convection in a differntially heated rotating fluid annulus. Geophys. Fluid Dyn. 7, 296–330.Google Scholar
Defant, A. 1961 Physical Oceanography. Pergamon.
Duncan, I. B. 1966 Axisymmetric convection between two rotating disks. J. Fluid Mech. 24, 417–449.Google Scholar
Fein, J. S. 1978 Boundary layers in Homogeneous and Stratified-Rotating Fluids. University Press of Florida.
Hide, R. 1969 In The Global Circulation of the Atmosphere (ed. G. A. Corby). London: Royal Met. Soc.
Hide, R. & Mason, P. J. 1975 Sloping convection in a rotating fluid. Adv. Phys. 24, 47–100.Google Scholar
Hignett, P. 1979 Experiments on thermal convection in a rotating fluid annulus, driven by non-uniform heating from below. Ph.D. dissertation, University of Reading.
Jeffreys, H. T. 1925 On fluid motions produced by differences of temperature and humidity. Quart. J. Roy. Met. Soc. 51, 347–356.Google Scholar
Killworth, P. D. & Manins, P. C. 1980 A model of confined thermal convection driven by non-uniform heating from below. J. Fluid Mech. 98, 587–607.Google Scholar
Mason, P. J. 1975 Baroclinic waves in a container with sloping end-walls. Phil. Trans. R. Soc. Lond. A, 278, 397–445.
Miller, R. C. 1968 A thermally convecting fluid heated non-uniformally from below. Ph.D. thesis, M.I.T.
Norman, A. C. 1972 A system for the solution of initial and two-point boundary value problems. Proc. Ass. Comp. Mach. (25th Anniv. Conf., Boston.), pp. 826–834.
Pedlosky, J. 1969 The linear theory of the circulation of a stratified ocean. J. Fluid Mech. 25, 185–205.Google Scholar
Rossby, H. T. 1965 On thermal convection driven by non-uniform heating from below. An experimental study. Deep-Sea Res. 12, 9–16.Google Scholar
Sandström, J. W. 1908 Dynamische Versuche mit Meerwasser. Ann. Hydr. Met. 6.Google Scholar
Stern, M. E. 1975 Ocean Circulation Physics. International Geophysics series, vol. 19. Academic.
Stommel, H. 1950 An example of thermal convection. Trans. Am. Geophys. Un. 31, 553–554.Google Scholar
Stommel, H. 1962 On the smallness of sinking regions in the ocean. Proc. Nat. Acad. Sci. 48, 766–772.Google Scholar
Tang, C. M. 1975 Stratified shear flows in the atmosphere and ocean. J. Geophys. Res. 80, 1168–1175.Google Scholar