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Ingersoll, A.P., and R.L. Miller, 1986: Motions in the interiors and atmospheres of Jupiter and Saturn: 2. Barotropic instabilities and normal modes of an adiabatic planet. Icarus, 65, 370-382, doi:10.1016/0019-1035(86)90144-2.
The low-frequency motions in a rotating, adiabatic, inviscid fluid planet are barotropic, quasi-geostrophic, and quasi-columnar. The only steady motions are differentially rotating cylinders in which zonal velocity ave(u) is a function of cylindrical radius r. Projected onto the planetary surface the limiting curvature at which the flow becomes unstable is negative; its amplitude is three to four times the amplitude for thin atmospheres, for planets in which density decreases linearly to zero at the surface. This result, derived first by A.P. Ingersoll and D. Pollard (1982, Icarus 52, 62-80) for low zonal wavenumber perturbations, is shown to hold for all quasi-columnar perturbations. When ave(u) = 0 the small amplitude motions are oscillatory. The lowest mode, as regards structure parallel to the axis, propagates eastward with a speed proportional to (wavelength)2. Both the barotropic stability criterion and the phase speed of the normal mode oscillations have features in common with Jupiter and Saturn observations, although the test is inconclusive with current data and theory.
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