Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence

Ricardo M. S. Rosa

Applications of Mathematics (2002)

  • Volume: 47, Issue: 6, page 485-516
  • ISSN: 0862-7940

Abstract

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Some rigorous results connected with the conventional statistical theory of turbulence in both the two- and three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding cascades. Some of the results are developed here in the case of nonsmooth boundaries and a less regular forcing term and for arbitrary stationary statistical solutions.

How to cite

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Rosa, Ricardo M. S.. "Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence." Applications of Mathematics 47.6 (2002): 485-516. <http://eudml.org/doc/33128>.

@article{Rosa2002,
abstract = {Some rigorous results connected with the conventional statistical theory of turbulence in both the two- and three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding cascades. Some of the results are developed here in the case of nonsmooth boundaries and a less regular forcing term and for arbitrary stationary statistical solutions.},
author = {Rosa, Ricardo M. S.},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; statistical solutions; turbulence; energy cascade; enstrophy cascade; Navier-Stokes equation; statistical solution; turbulence; energy cascade; enstrophy cascade},
language = {eng},
number = {6},
pages = {485-516},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence},
url = {http://eudml.org/doc/33128},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Rosa, Ricardo M. S.
TI - Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 6
SP - 485
EP - 516
AB - Some rigorous results connected with the conventional statistical theory of turbulence in both the two- and three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding cascades. Some of the results are developed here in the case of nonsmooth boundaries and a less regular forcing term and for arbitrary stationary statistical solutions.
LA - eng
KW - Navier-Stokes equations; statistical solutions; turbulence; energy cascade; enstrophy cascade; Navier-Stokes equation; statistical solution; turbulence; energy cascade; enstrophy cascade
UR - http://eudml.org/doc/33128
ER -

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