This thesis consists of two papers on the dynamics of Jovian planet atmospheres. The first paper discusses the uses of a normal-mode expansion in the vertical for modelingthe dynamics of Jupiter's atmosphere. The second paper uses a non-linear numerical model based on the normal-mode expansion of the first paper to study the dynamicsof baroclinic vortices. The abstracts for the two papers are reproduced below.
Paper 1:
We propose a non-linear, quasi-geostrophic, baroclinic model of Jovian atmospheric dynamics, in which vertical variations of velocity are represented by a truncated sum over a complete set of orthogonal functions obtained by a separation of variables of the linearized quasi-geostrophic potential vorticity equation. A set of equations for the time variation of the mode amplitudes in the non-linear case is then derived. We show that for a planet with a neutrally stable, fluid interior instead of a solid lower boundary, the barotropic mode represents motions in the interior, and is not affected by the baroclinic modes. One consequence of this is that a normal mode model with one baroclinic mode is dynamically equivalent to a one layer model with solid lower topography. We also show that for motions in Jupiter's cloudy lower troposphere, the stratosphere behaves nearly as a rigid lid, so that the normal-mode model is applicable to Jupiter. We test the accuracy of the normal-mode model for Jupiter using two simple problems: forced, vertically propagating Rossby waves, using two and three baroclinic modes, and baroclinic instability, using two baroclinic modes. We find that the normal-mode model provides qualitatively correct results,even with only a very limited number of vertical degrees of freedom.
Paper 2:
We examine the evolution of baroclinic vortices in a time dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes (Achterberg and Ingersoll 1989). Our results for the stability of baroclinic vortices on an ƒ-plane in the absence of a mean zonal flow are consistent with previous results in the literature, although the presence of the deep fluid interior on the Jovian planets appears to shift the stability boundaries to smaller length scales. The presence of a mean zonal shear flow acts to stabilize vortices against instability, significantly modifiesthe finite amplitude form of baroclinic instabilities, and combined with internal barotropic instability (Gent and McWilliams 1986) produces periodic oscillations in thelatitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations ofvortices on the outer planets. Oscillations in aspect ratio and orientation of stable elliptical vortices in a zonal shear flow are observed in this baroclinic model, as insimpler two-dimensional models (Kida 1981). The meridional propagation and decay of vortices on a β-plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of Jupiter.
