Entropy, closures and subgrid modeling

Maximum entropy states or statistical mechanical equilibrium solutions have played an important role in the development of a fundamental understanding of turbulence and its role in geophysical flows. In modern general circulation models of the earth's atmosphere and oceans most parameterizations of the subgrid-scale energy and enstrophy transfers are based on ad hoc methods or ideas developed from equilibrium statistical mechanics or entropy production hypotheses. In this paper we review recent developments in nonequilibrium statistical dynamical closure theory, its application to subgrid-scale modeling of eddy-eddy, eddy-mean field and eddy-topographic interactions and the relationship to minimum enstrophy, maximum entropy and entropy production arguments.