Friction Term Formulation and Convective Instability in a Shallow Atmosphere

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(?H/?V)½ are produced, where ?H, ?V are the horizontal and vertical diffusion coefficients. The critical Rayleigh number is given by Rc=4π4?H/?V, but another Rayleigh number P=?g?Td5/(?V?VL), 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.