A Fully Nonlinear, Mixed Spectral and Finite Difference Model for Thermally Driven, Rotating Flows

A model which can simulate a variety of thermally driven, rotating flows in cylindrical and spherical geometries is described. The technique used to approximate the Navier-Stokes equations is finite difference in time and in the meridional plane, and spectral in the azimuthal direction. The model can calculate axisymmetric flow, linearized waves with respect to a fixed or a changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully non-linear three-dimensional flow. Detailed numerical studies are made to reexamine the steady baroclinic wave case previously investigated by Williams [ J. Fluid Mech.49, 417 (1971) ] and by Quon [ J. Comp. Phys.20, 442 (1976)] . With one or more harmonic waves added to the fundamental wave 5, the present model in fully nonlinear mode agrees very well with Williams. With only a single wave, disagreement exists between the present model and that of Quon on the amplitude of the wave and its effects on the azimuthal mean circulation. New studies on wavenumber selection using the present model indicate that the results for this case depend on the initial conditions.