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Finite difference numerical models based upon the Navier-Stokes equations with the Boussinesq approximation have been utilized to study the dynamics of a rotating liquid with horizontal density gradients. There are two configurations analyzed: a cylindrical annulus of water rotating about a vertical axis (parallel to the body force), and a hemispherical shell of silicone oil with a radial body force, rotating about the polar axis. In both the cylindrical and spherical configurations, the thermal and mechanical forcings (boundary conditions) are symmetric about the axis of rotation. The physical parameters varied are the rotation rate and the amplitude of the horizontal thermal forcing. Two numerical models have been developed for each geometrical configuration: one to calculate axisymmetric flows and another to test the stability of those flows to non-axisymmetric perturbations. The primary purpose of the models is to determine whether axisymmetric or non-axisymmetric flow will be observed in a corresponding laboratory experiment. For the cylindrical annulus, the predictions of axisymmetric and non-axisymmetric flow are in good agreement with laboratory experiments previously performed. In the spherical experiment considered, which has not been performed in the laboratory, there is evidence that if the rotation rate is fixed and the latitudinal thermal forcing is reduced, there exists a transition from non-axisymmetric to axisymmetric flow, but that as the rotation rate is decreased for a fixed latitudinal thermal gradient on the boundaries, the flow does not become axisymmetric. The structures of some of the fastest growing eigenmodes are presented for both cylindrical and spherical cases. Analyses of the energetics indicate that the waves in all cases considered are essentially baroclinic in nature.

A variety of general circulation model experiments are performed to investigate the influence of seasonality and topography on the strength of baroclinic eddies in the Martian atmosphere. Three different models are used: a full physics model, a simplified physics model, and a zonally symmetric simplified physics model. All three models are sigma coordinate, finite difference global atmospheric circulation models that have been adapted to the Martian regime. The full physics model has previously been tested extensively by researchers at the NASA Ames Research Center. The simplified physics model replaces many of the atmospheric physics routines with simple parameterizations; most importantly, the radiation code is replaced by Newtonian cooling. A Newtonian cooling code with a radiative time constant that varies in height and latitude produces superior results to one with a radiative time constant that is the same everywhere throughout the atmosphere. It is found that baroclinic eddy activity is extremely sensitive to the mean meridional temperature gradient in the simplified model. A power law fit gives an exponent of approximately six. The baroclinic eddy activity is also sensitive to the maximum growth rate in the Eady model of baroclinic activity. This is due to the close connection between the meridional temperature gradient and the maximum growth rate. Baroclinic adjustment theory, which predicts how baroclinic eddies will react to changes in the mean circulation, does not appear to be valid in the Martian regime, according to the simplified model. This finding may be related to the differences in the relative strengths of the baroclinic eddies and the mean circulation on Earth and Mars. The simplified model indicates that seasonality is more important than topography in creating stronger eddies in the northern hemisphere winter than in the southern hemisphere winter. However, the effects of topography in the simplified model may not be adequately matching the effects of topography in the full physics model, particularly in the southern hemisphere. / Graduation date: 2001