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An experimental study of the effects of Prandtl number on thermal convection in a rotating, differentially heated cylindrical annulus of fluid

Published online by Cambridge University Press:  29 March 2006

Jay S. Fein  and
Richard L. Pfeffer
Jay S. Fein
Affiliation:
Geophysical Fluid Dynamics Institute and Department of Meteorology, Florida State University, Tallahassee Present address: Department of Meteorology, University of Oklahoma, Norman, Oklahoma 73069.
Richard L. Pfeffer
Affiliation:
Geophysical Fluid Dynamics Institute and Department of Meteorology, Florida State University, Tallahassee
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Abstract

This paper presents the results of experimental studies of the behaviour of different fluids (mercury, Pr = 0·0246; water, Pr = 7·16; and 5 cS silicone oil, Pr = 63) when each is contained in a rotating cylindrical annulus and subjected to an imposed radial temperature difference across the annulus. The results are summarized in the form of two-parameter regime diagrams (thermal Rossby number RoTvs. Taylor number Ta) at different Prandtl numbers Pr. The fluids are in contact above and below with rigid insulating boundaries. The range of thermal Rossby and Taylor numbers surveyed is 10−3 < RoT < 10, 105 < Ta < 109.

The regime diagram for water with a rigid upper lid in contact with the fluid resembles in certain respects the more familiar regime diagram for water with a free upper surface obtained by Fultz (1956) and by Fowlis & Hide (1965). Significant differences do, however, occur and are discussed in a separate paper by Fein (1973). The regime diagram for silicone oil possesses no lower symmetric regime within the range of thermal Rossby and Taylor numbers surveyed; that for mercury possesses no upper symmetric regime within the range surveyed. In mercury, turbulence is observed at high Rossby numbers. An experimental traverse across the regime diagram in which the imposed temperature difference is held constant at ΔT = 5 °C and the rotation rate Ω is changed monotonically reveals a highly conductive temperature structure in mercury and a highly convective temperature structure in both water and silicone oil. The regular wave regime, which appears at all three Prandtl numbers, is found to shift towards higher Taylor and Rossby numbers with decreasing Prandtl number. As a result, a single point in two-dimensionless-parameter space (RoT = 5 × 10−1, Ta = 1 × 106) lies in the upper symmetric regime for 5 cS silicone oil (Pr = 63), in the regular wave regime for water (Pr = 7·16) and in the lower symmetric regime for mercury (Pr = 0·0246).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 1 , 13 May 1976 , pp. 81 - 112
Copyright
© 1976 Cambridge University Press

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References

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
Douglas, H. A. & Mason, P. J. 1973 Thermal convection in a large rotating fluid annulus: some effects of varying the aspect ratio. J. Atmos. Sci. 30, 1124–810.Google Scholar
Fein, J. S. 1973 An experimental study of the effects of the upper boundary condition on the thermal convection in a rotating, differentially heated cylindrical annulus of fluid Geophys. Fluid Dyn. 5, 213–248.Google Scholar
Fowlis, W. W. 1970 Techniques and apparatus for the fast and accurate measurement of fluid temperature and flow speed fields Rev. Sci. Instrum. 41, 570–576.Google Scholar
Fowlis, W. W. & Hide, R. 1965 Thermal convection in a rotating annulus of liquid: effect of viscosity on the transition between axisymmetric and non-axisymmetric flow regimes. J. Atmos. Sci. 22, 541–810.Google Scholar
Fowlis, W. W. & Rossby, H. T. 1964 A compilation of selected data on the temperature dependence of some physical properties of water, glycerol-water solutions and mercury. Hydrodyn. Rotating Fluids Project, Dept. Geology Geophys. M.I.T., Lab. Note, HRF/LN4.
Fultz, D. 1956 A survey of certain thermally and mechanically driven fluid systems of meteorological interest. Fluid Models in Geophysics, pp. 27–63. U.S. Govt Printing Office.
Fultz, D., Long, R. R., Owens, G. V., Bohan, W., Kaylor, R. & Weil, J. 1959 Studies of thermal convection in a rotating cylinder with some implications for large-scale atmospheric motions. Meteor. Monograph, 4. Boston: Am. Met. Soc.
Hide, R. 1953 Some experiments on thermal convection in a rotating liquid Quart. J. Roy. Met. Soc. 79, 161.Google Scholar
Hide, R. 1958 An experimental study of thermal convection in a rotating liquid. Phil. Trans A 250, 441–478.Google Scholar
Hide, R. 1969 Some laboratory experiments on free thermal convection in a rotating fluid subject to a horizontal temperature gradient and their relation to the theory of the global atmospheric circulation. The Global Circulation of the Atmosphere (ed. G. A. Corby), pp. 196–221. London: Roy. Met. Soc.
Hide, R. & Mason, P. J. 1975 Sloping convection in a rotating fluid Adv. in Phys. 24, 47–100.Google Scholar
Mason, P. J. 1976 Baroclinic waves in a container with sloping end walls. Phil. Trans. A (in press).Google Scholar