Product-sum conversion of spherical harmonics with application to thermal convection

Details Product-sum conversion of spherical harmonics with application to thermal convection Product-sum conversion of spherical harmonics with application to thermal convection

Jan 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975jgr....80..225k&link_type=abstract

Journal of Geophysical Research, vol. 80, Jan. 10, 1975, p. 225-231.

Physics

3

Free Convection, Mathematical Models, Newtonian Fluids, Spherical Harmonics, Viscous Fluids, Computer Programs, Differential Equations, Gravitational Fields, Heuristic Methods, Nonlinearity, Poisson Equation, Products, Quadratic Equations, Sums, Tensor Analysis

Scientific paper

A single closed expression is derived for the product-sum conversion of spherical harmonics and their derivatives to any order. The equations for thermal convection in a sphere at an infinite Prandtl number are transformed to a set of quadratic first-order ordinary differential equations suitable for numerical integration with respect to radius. The product-sum formulas are applied to the quadratic terms arising from advection, dissipation, and the linear temperature dependence of viscosity.

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