The Regime Transition and the Horizontal Scale of Rotating Convection based on Two-Dimensional Numerical Experiments
(Saitama Institute of Technology, Department of Mechanical Engineering)
Abstract:Horizontal scales of rotating convection are investigated using a two-dimensional numerical model, with special emphasis on the scaling laws derived by Sakai. In cases where rigid boundary conditions are imposed both on the top and the bottom surfaces, dependencies on Rayleigh number (Ra) and Taylor number (Ta) show that the horizontal scale becomes larger as Ra becomes larger, whereas it is not monotonically dependent on Ta; there is a maximum in the horizontal scale when Ta is changed. This type of dependency on Ta is apparently consistent with that given by Sakai's law. However, detailed analysis of balances in the horizontal momentum equation shows that as Ta becomes larger, a transition occurs from the "friction regime", in which the friction term is important, to the "geostrophic regime", in which the Coriolis term is dominant. The horizontal scale becomes smaller when the regime of convection switches from the friction regime to the geostrophic regime. In particular, in cases of sufficiently larger Raileygh numbers than those of the neutral states (Ra = 105, 106 ), the transition occurs at a larger Taylor number than that predicted by the linear theory. It should be noted that there are cases in which convection is turbulent and unsteady between the two regimes. Sakai assumed the geostrophic balance in his scaling argument, so that the maximum of the horizontal scale obtained by the present experiments does not correspond to that given by Sakai's theory. For cases of the geostrophic regime, however, the horizontal scales are well described by Sakai's theory.
Dependencies on the different kinds of boundary conditions have also been investigated. The horizontal scales are generally larger in cases of the slippery boundary conditions than in cases of the rigid boundary conditions. In the slippery cases, the horizontal scales are gradually broadened with time. It has been found that the Nusselt number becomes smaller when two successive convective cells are merged.
Received 13 January, 1998; in revised form 14 April, 1998