Potential Vorticity and Layer Thickness Variations in the Flow around Jupiter's Great Red Spot and White Oval BC

Abstract

Layer thickness variations in Jupiter's atmosphere are investigated by treating potential vorticity as a conserved tracer. Starting with the horizontal velocity field measured from Voyager images, fluid trajectories around the Great Red Spot (GRS) and White Oval BC are calculated. The flow is assumed to be frictionless, adiabatic, hydrostatic, and steady in the reference frame of the vortex. Absolute vorticity is followed along each trajectory; its magnitude is assumed to vary directly as the thickness, which is defined as the mass per unit area between potential temperature surfaces. To the accuracy of the observations. the inferred thickness is a separable function of trajectory and latitude. The latitude dependence has positive curvature near the GRS and BC. The relative variations of thickness with respect to latitude are generally larger than the relative variations of Coriolis parameter with respect to latitude—the beta effect. The data are a useful diagnostic which will help differentiate between models, of Jovian vortices. The present analysis employs a quasi-geostrophic model in which a thin upper weather layer, which contains the vortex, is supported hydrostatically by a much deeper lower layer. In this model, the upper free surface does not contribute to the observed variation of thickness along trajectories. Such variations are due exclusively to bottom topography—flow of the deep lower layer relative to the vortex. The observation are used to infer the form of the deep zonal velocity profile vs. latitude. The magnitude of the profile depends on the unknown static stability. The principal result is the existence of horizontal shear in the deep layer zonal velocity profile, i.e., the lower layer is not in solid body rotation and does not act like a flat solid surface. In this respect the data support the hypothesis of Ingersoll and Cuong concerning motions in the deep layer. However at some latitudes the data violate Ingersoll and Cuong's criterion governing the compactness of the vortices. At these latitudes the topography allows standing Rossby waves (wakes) extending far downstream to the west. Observed wavelike features, the filamentary regions, are possibly formed by this mechanism.

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