SYMMETRICAL DISTURBANCES IN A THIN LAYER OF FLUID SUBJECT TO A HORIZONTAL TEMPERATURE GRADIENT AND ROTATION

Abstract

The symmetrical thermal convection of a rotating fluid subject to a horizontal temperature difference is examined. It is shown that the effect of rotation is to inhibit the convection. The extent of this inhibition depends upon the non-dimensional parameter T = 4Ω2d4v?2, where d denotes the depth of the layer, Ω the rotation rate, and ? is the kinematic viscosity. For a given value of T, the onset of convection requires the non-dimensional parameter Q = gd4 ?? (k?a??1 to be higher than a critical value Qc, and there is a most favorable cell size lc, for which the critical Q is lowest. Here ??1 ?? is the horizontal density contrast, k the thermometric conductivity, and a is horizontal extent (radius of the pan used). When T is very large, 4Qd(lT)?1 approaches a constant value, suggesting that the onset of convection may be determined by the product of a properly defined Rossby number and the Prandtl number, ?k?1. The forms of the flow pattern and the temperature distribution are also discussed.