E-mail: edward.bolton@yale.edu

Orthogonal Basis Functions for Spherical Shell Convection

As previous Galerkin codes for spherical shell convection were based on nonorthogonal radial expansion functions, I have developed an orthogonal radial basis set for the poloidal velocity field, which satisfies two boundary conditions at each spherical surface. For the perturbation temperature and toroidal velocity fields, a combination of spherical Bessel functions of the first and second kind yield a radial basis set. I have also derived a family of orthogonal polynomial basis functions which appear to better resolve the radial structure [Bolton, 1992, abst.].

E.W. Bolton, Radial functions for spectral/Galerkin modeling of spherical-shell convection, EOS, Trans of Am. Geoph. Union, 73, p. 575 of Fall 1992 AGU Meeting Supplement, 1992.