dorsal/arxiv
View SchemaOpportunities for use of exact statistical equations
| Authors | Reginald J. Hill |
|---|---|
| Categories | |
| ArXiv ID | physics/0512038 |
| URL | https://arxiv.org/abs/physics/0512038 |
| DOI | 10.1080/14685240600595636 |
Abstract
Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.
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"abstract": "Exact structure function equations are an efficient means of obtaining\nasymptotic laws such as inertial range laws, as well as all measurable effects\nof inhomogeneity and anisotropy that cause deviations from such laws. \"Exact\"\nmeans that the equations are obtained from the Navier-Stokes equation or other\nhydrodynamic equations without any approximation. A pragmatic definition of\nlocal homogeneity lies within the exact equations because terms that explicitly\ndepend on the rate of change of measurement location appear within the exact\nequations; an analogous statement is true for local stationarity. An exact\ndefinition of averaging operations is required for the exact equations. Careful\nderivations of several inertial range laws have appeared in the literature\nrecently in the form of theorems. These theorems give the relationships of the\nenergy dissipation rate to the structure function of acceleration increment\nmultiplied by velocity increment and to both the trace of and the components of\nthe third-order velocity structure functions. These laws are efficiently\nderived from the exact velocity structure function equations. In some respects,\nthe results obtained herein differ from the previous theorems. The\nacceleration-velocity structure function is useful for obtaining the energy\ndissipation rate in particle tracking experiments provided that the effects of\ninhomogeneity are estimated by means of displacing the measurement location.",
"arxiv_id": "physics/0512038",
"authors": [
"Reginald J. Hill"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1080/14685240600595636",
"title": "Opportunities for use of exact statistical equations",
"url": "https://arxiv.org/abs/physics/0512038"
},
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