2002/03/11 by Gregory W. Hammett, G. W. Hammett, Hammett, Gregory W. +2
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Plasma Physics (physics.plasm-ph) #Statistical Mechanics and Entropy #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.physics/0203031
23 pages, LaTeX, submitted to Physics of Fluids. Maple worksheets available at http://w3.pppl.gov/~hammett/papers/2002/
arxiv created 2002/03/11 · openalex publication_date 2002/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.