  Manifestly Markovian closures for the interaction of two-dimensional
inhomogeneous turbulent flows with Rossby waves and topography are formulated
and compared with large ensembles of direct numerical simulations (DNS) on a
generalized beta plane. Three versions of the Markovian inhomogeneous closure
(MIC) are established from the quasi-diagonal direct interaction approximation
(QDIA) theory by modifying the response function to a Markovian form and
employing respectively the current-time (quasi-stationary) fluctuation
dissipation theorem (FDT), the prior-time (non-stationary) FDT and the
correlation FDT. Markov equations for the triad relaxation functions are
derived that carry similar information to the time-history integrals of the
non-Markovian QDIA closure but become relatively more efficient for long
integrations. Far from equilibrium processes are studied, where the impact of a
westerly mean flow on a conical mountain generates large amplitude Rossby waves
in a turbulent environment, over a period of 10 days. Excellent agreement
between the evolved mean streamfunction and mean and transient kinetic energy
spectra are found for the three versions of the MIC and two variants of the
non-Markovian QDIA compared with an ensemble of 1800 DNS. In all cases mean
Rossby wavetrain pattern correlations between the closures and the DNS ensemble
are greater than 0.9998.
