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

Author:

Hignett Phillip,Ibbetson Alan,Killworth Peter D.

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.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference23 articles.

1. Daniels, P. G. 1976 Thermal convection in a differntially heated rotating fluid annulus.Geophys. Fluid Dyn. 7,296–330.

2. Stommel, H. 1950 An example of thermal convection.Trans. Am. Geophys. Un. 31,553–554.

3. Duncan, I. B. 1966 Axisymmetric convection between two rotating disks.J. Fluid Mech. 24,417–449.

4. 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.

5. Mason, P. J. 1975 Baroclinic waves in a container with sloping end-walls. Phil. Trans. R. Soc. Lond . A, 278, 397–445.

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