Abstract
The form of the friction terms for a shallow layer of fluid on a sphere is discussed for isotropic and transversely-isotropic fluids. We then examine the nature of convection in a transversely-isotropic fluid and find that long flat convection cells with a width to height ratio of 2(νH/νV)½ are produced, where νH, νV are the horizontal and vertical diffusion coefficients. The critical Rayleigh number is given by Rc=4π4νH/νV, but another Rayleigh number P=βgΔTd5/(νVκVL), with a constant critical value Rc=4π4 is shown to be a more relevant parameter. Results for convection in a rotating system are also given.
