Spectral methods for the simulation of incompressible flows in spherical shells

A spatial discretization of the incompressible Navier-Stokes equation is pr esented in which the velocity is decomposed using poloidal and toroidal sca lars whose spatial dependence is given in terms of spherical harmonics and Chebychev polynomials. The radial resolution needs to be large enough at an y given angular resolution in order to avoid instability in the simulation of rotating flows. Several semi-implicit time steps are discussed. The most accurate scheme is an integrating factor technique. Copyright (C) 1999 Joh n Wiley & Sons, Ltd.