Realizable Eddy Damped Markovian Anisotropic Closure for Turbulence and Rossby Wave Interactions

A realizable Eddy Damped Markovian Anisotropic Closure (EDMAC) is presented for the interaction of two-dimensional turbulence and transient waves such as Rossby waves. The structure of the EDMAC ensures that it is as computationally efficient as the eddy damped quasi normal Markovian (EDQNM) closure but, unlike the EDQNM, is guaranteed to be realizable in the presence of transient waves. Jack Herring's important contributions to laying the foundations of statistical dynamical closure theories of fluid turbulence are briefly reviewed. The topics covered include equilibrium statistical mechanics, Eulerian and quasi-Lagrangian statistical dynamical closure theories, and the statistical dynamics of interactions of turbulence with topography. The impact of Herring's work is described and placed in the context of related developments. Some of the further works that have built upon Herring's foundations are discussed. The relationships between theoretical approaches employed in statistical classical and quantum field theories, and their overlap, are outlined. The seminal advances made by the pioneers in strong interaction fluid turbulence theory are put in perspective by comparing related developments in strong interaction quantum field theory.