Jupiter's Great Red Spot as a Shallow Water System

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Abstract
Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravi... Abstract Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravi...

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