  The theoretical basis for the Eddy Damped Markovian Anisotropic Closure
(EDMAC) is formulated for two-dimensional anisotropic turbulence interacting
with Rossby waves in the presence of advection by a large-scale mean flow. The
EDMAC is as computationally efficient as the Eddy Damped Quasi Normal Markovian
(EDQNM) closure but in contrast is realizable in the presence of transient
waves. The EDMAC is arrived at through systematic simplification of a
generalization of the non-Markovian Direct Interaction Approximation (DIA)
closure that has its origin in renormalized perturbation theory. Markovian
Anisotropic Closures (MACs) are obtained from the DIA by using three variants
of the Fluctuation Dissipation Theorem (FDT) with the information in the time
history integrals instead carried by Markovian differential equations for two
relaxation functions. One of the MACs is simplified to the EDMAC with
analytical relaxation functions and high numerical efficiency, like the EDQNM.
Sufficient conditions for the EDMAC to be realizable in the presence of Rossby
waves are determined. Examples of the numerical integration of the EDMAC
compared with the EDQNM are presented for two-dimensional isotropic and
anisotropic turbulence, at moderate Reynolds numbers, possibly interacting with
Rossby waves and large-scale mean flow. The generalization of the EDMAC for the
statistical dynamics of other physical systems, to higher dimension and higher
order nonlinearity is considered.
