Friction Term Formulation and Convective Instability in a Shallow Atmosphere

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  • 1 Geophysical Fluid Dynamics Laboratory, NOAA, Princeton University, Princeton, N.J. 08540
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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(νHV)½ are produced, where νH, νV are the horizontal and vertical diffusion coefficients. The critical Rayleigh number is given by Rc=4π4νHV, 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.

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(νHV)½ are produced, where νH, νV are the horizontal and vertical diffusion coefficients. The critical Rayleigh number is given by Rc=4π4νHV, 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.

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