I will describe recent work with Majda, Haven and DiBattista
(PNAS 98:12346-12350, 2001) in which we give the first
quantitative comparison between the predictions of a statistical
equilibrium theory of coherent structures and the observations
by the Voyager and Galileo missions of the active weather layer
on Jupiter. In this theory the unresolved small scales are
parameterized by a prior probability distribution on potential
vorticity fluctuations. The results imply that this prior
distribution has anticyclonic skewness -- intense anticyclones
predominate among the eddies. The predicted most probable states
of the observed layer are then zonal jets and anticyclonic
vortices embedded in those jets. For midlatitude bands in the
northern and southern hemisphere, these equilibrium states agree
with the observed wind field on the large scales. The nonlinear
stability of these states is also demonstrated, using a new
refinement of Arnold's Lyapunov argument. This application
suggests using statistical equilibrium theory for inverse
modeling of the small-scale charateristics of geophysical
turbulence from observed large-scale features.
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