13.1 Introduction

Prominent examples of long-lived large-scale vortices in geophysical flows are those such as the Great Red Spot (GRS) on Jupiter (Dowling, 1995; Marcus, 1993; Rogers, 1995). The emergence and persistence of such coherent structures at specific latitudes such as 22.4 S for the GRS in a background zonal shear flow that seems to violate all of the standard stability criteria (Dowling, 1995) are a genuine puzzle. Here we show how to utilize the equilibrium statistical theory with a suitable prior distribution, ESTP, introduced in Section 9.2 and discussed in Chapters 10, 11, and 12 to predict the actual coherent structures on Jupiter in a fashion which is consistent with the known observational record. As discussed in Section 9.2, the statistical theory is based on a few judiciously chosen conserved quantities for the inviscid dynamics such as energy and circulation and does not involve any detailed resolution of the fluid dynamics. The key ingredient of the ESTP is the prior distribution, ?( ?), for the one-point statistics of the potential vorticity which parameterizes the unresolved small-scale turbulent eddies that produce the large-scale coherent structures. Below, we show how the observational record of Jupiter from the recent Galileo mission suggests a special structure for such a prior distribution resulting from intense small-scale forcing. Recall from the studies discussed in Chapter 12 (DiBattista, Majda, and Grote, 2001) that ESTP can potentially describe the meta-stable large-scale coherent structures occurring from strong small-scale forcing, provided that the flux of energy to...