Introduction

A major theme of Chapters 6–13 of this book is to illustrate that systematic application of ideas from equilibrium statistical mechanics leads to novel promising strategies for assessing the unresolved scales of motion in geophysical flows. The various theories range from the simplest energy–enstrophy statistical theory (EEST) discussed in Chapters 6 and 8 to the empirical statistical theories discussed in Section 9.4 attempting to encode all the conserved quantities (ESTMC), to point vortex statistical theories discussed in Section 9.3, and, finally, to the empirical statistical theories with a few large-scale constraints and a judicious small-scale prior distribution (ESTP) formulated in Section 9.2. It was established in Chapters 11, 12, and 13 that the ESTP theories have a wide range of applicability in predicting large-scale behavior in damped and driven flows, as well as for observations such as the Great Red Spot of Jupiter. The ESTP formulation also includes the predictions of the energy–enstrophy statistical theory for the mean flow from Chapters 6 and 8 by utilizing a simple Gaussian prior probability distribution for potential vorticity fluctuations.

As discussed earlier, in Chapters 8, 9, and 10, the different equilibrium statistical theories all attempt to predict the coarse-grained behavior at large scales through the use of some of the formally infinite list of conserved quantities for idealized geophysical flows derived in Chapter 1.