  Markovian models of turbulence can be derived from the renormalized
statistical closure equations of the direct-interaction approximation (DIA).
Various simplifications are often introduced, including an assumption that the
two-time correlation function is proportional to the renormalized infinitesimal
propagator (Green's function), i.e. the decorrelation rate for fluctuations is
equal to the decay rate for perturbations. While this is a rigorous result of
the fluctuation--dissipation theorem for thermal equilibrium, it does not
necessarily apply to all types of turbulence. Building on previous work on
realizable Markovian closures, we explore a way to allow the decorrelation and
decay rates to differ (which in some cases affords a more accurate treatment of
effects such as non-white noise), while retaining the computational advantages
of a Markovian approximation. Some Markovian approximations differ only in the
initial transient phase, but the multiple-rate Markovian closure (MRMC)
presented here could modify the steady-state spectra as well. Markovian models
can be used directly in studying turbulence in a wide range of physical
problems (including zonal flows, of recent interest in plasma physics), or they
may be a useful starting point for deriving subgrid turbulence models for
computer simulations.
