The horizontal scale of rotating convection in the geostrophic regime

Abstract

The horizontal scale of rotating convection with rigid boundary conditions is studied. The range of Rayleigh number concerned is moderate, i.e. large enough to induce a finite-amplitude convection but small enough so that the geostrophic processes are significant.On considering an experimental law of the Nusselt number and some constraints of elemental geostrophic processes, the horizontal scale of the convection can be estimated. This estimation strongly depends on the ratio between the thicknesses of the Ekman layer and the thermal boundary layer, and does not depend monotonically on the Rayleigh number. This dependency is compatible with the experimental results of Rossby (1969).The estimated horizontal scale was checked by laboratory experiments. The horizontal temperature distribution was visualized by thermal liquid-crystal capsules dispersed in the working fluid. The horizontal scale was measured by counting vortices. The experimental results agree fairly well with the estimated scale.