A Normal-Mode Approach to Jovian Atmospheric Dynamics

We propose a nonlinear, 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 quation. A set of equations for the time variation of the mode amplitudes in the nonlinear case is then derived. We show that for a planet with a neutrally stable, fluid interior instead of a solid lower boundary, the barotropc mode mxesents motions in the interior, and is not affected by the baroclinic modes. One consequence of this is that a normalmode 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 nonnal-mode model is applicable to Jupiter. We test the accuracy of the normal-mode model for Jupiter using two simple problems: forced, vertically propagating Roasby 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 W s of freedom.