2D turbulence in physical scales of the NavierStokes equations
Abstract
Local analysis of the two dimensional NavierStokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the size of the domain. In the framework of zero driving force and nonincreasing global energy, these bounds produce sufficient conditions for existence of the direct enstrophy and inverse energy cascades. Several manifestations of locality of the fluxes under these conditions are obtained. All the scales involved are actual physical scales in R^2 and no homogeneity assumptions are made.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 arXiv:
 arXiv:1101.2209
 Bibcode:
 2011arXiv1101.2209D
 Keywords:

 Mathematics  Analysis of PDEs;
 Physics  Fluid Dynamics;
 35Q30;
 76D05;
 76F02
 EPrint:
 24 pages, 3 figures