Non-white noise and a multiple-rate Markovian closure theory for turbulence

Details Non-white noise and a multiple-rate Markovian closure theory for turbulence Non-white noise and a multiple-rate Markovian closure theory for turbulence

2002-03-11

arxiv.org/abs/physics/0203031v1

Physics

Fluid Dynamics

23 pages, LaTeX, submitted to Physics of Fluids. Maple worksheets available at http://w3.pppl.gov/~hammett/papers/2002/

Scientific paper

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.

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