dorsal/arxiv
View SchemaNon-white noise and a multiple-rate Markovian closure theory for turbulence
| Authors | Gregory W. Hammett, John C. Bowman |
|---|---|
| Categories | |
| ArXiv ID | physics/0203031 |
| URL | https://arxiv.org/abs/physics/0203031 |
Abstract
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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"abstract": "Markovian models of turbulence can be derived from the renormalized\nstatistical closure equations of the direct-interaction approximation (DIA).\nVarious simplifications are often introduced, including an assumption that the\ntwo-time correlation function is proportional to the renormalized infinitesimal\npropagator (Green\u0027s function), i.e. the decorrelation rate for fluctuations is\nequal to the decay rate for perturbations. While this is a rigorous result of\nthe fluctuation--dissipation theorem for thermal equilibrium, it does not\nnecessarily apply to all types of turbulence. Building on previous work on\nrealizable Markovian closures, we explore a way to allow the decorrelation and\ndecay rates to differ (which in some cases affords a more accurate treatment of\neffects such as non-white noise), while retaining the computational advantages\nof a Markovian approximation. Some Markovian approximations differ only in the\ninitial transient phase, but the multiple-rate Markovian closure (MRMC)\npresented here could modify the steady-state spectra as well. Markovian models\ncan be used directly in studying turbulence in a wide range of physical\nproblems (including zonal flows, of recent interest in plasma physics), or they\nmay be a useful starting point for deriving subgrid turbulence models for\ncomputer simulations.",
"arxiv_id": "physics/0203031",
"authors": [
"Gregory W. Hammett",
"John C. Bowman"
],
"categories": [
"physics.flu-dyn",
"physics.plasm-ph"
],
"title": "Non-white noise and a multiple-rate Markovian closure theory for turbulence",
"url": "https://arxiv.org/abs/physics/0203031"
},
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