Abstract
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 earthâs 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.
Highlights
The complexity of geophysical flows has made the understanding of the dynamics of the oceans and the atmosphere difficult
We present a discussion of the equilibrium statistical mechanics of Rossby wave turbulence and general mean flows over topography on a generalized β-plane as developed by Frederiksen & OâKane (2005) [99]
The nonequilibrium statistical dynamical QDIA closure theory (Frederiksen (1999) [98]) has been extensively tested and in regularized form is in excellent agreement with results of direct numerical simulations of general mean flows interacting with inhomogeneous turbulence, Rossby waves and topography (OâKane & Frederiksen (2004) [88] and Frederiksen & OâKane (2005) [99]) and in predictability studies (OâKane & Frederiksen (2008a) [71])
Summary
The complexity of geophysical flows has made the understanding of the dynamics of the oceans and the atmosphere difficult. Canonical equilibrium states are exact statistically steady states for the DIA and QDIA closures and there is a general increase of entropy in DNS toward equilibrium not always monotonically, as discussed by Frederiksen & Bell (1983) [105], (1984) [106] for the internal gravity wave-turbulence problem These authors and others (Kleeman (2002) [107] and references therein) have used entropy as a measure of dynamical development and predictability. Frederiksen & Davies (1997) [57] developed representations of eddy viscosity and stochastic backscatter based on EDQNM and DIA closure models for barotropic turbulent flows on the sphere They found that their parameterizations cured the typical resolution dependence of atmospheric energy spectra with LES incorporating the parameterizations being in close agreement with higher resolution barotropic DNS.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
