On universal relations in 2-D turbulence

Nusret Balci; Ciprian Foias; M. S Jolly; Ricardo Rosa

doi:10.3934/dcds.2010.27.1327

Article Contents

2010, Volume 27, Issue 4: 1327-1351. Doi: 10.3934/dcds.2010.27.1327

This issue Previous Article Solitary-wave solutions to Boussinesq systems with large surface tension Next Article Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations

On universal relations in 2-D turbulence

1.
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455
2.
Department of Mathematics, Texas A&M University, College Station, TX 77843
3.
Department of Mathematics, Indiana University, Bloomington, IN, 47405
4.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Ilha do Fundão, Rio de Janeiro, RJ 21941-909

Received: February 2010

Revised: March 2010

Published: December 2010

Abstract Related Papers Cited by

Abstract

A rigorous study of universal laws of 2-D turbulence is presented for time independent forcing at all length scales. Conditions for energy and enstrophy cascades are derived, both for a general force, and for one with a large gap in its spectrum. It is shown in the gap case that either a direct cascade of enstrophy or an inverse cascade of energy must hold, provided the gap modes of the velocity has a nonzero ensemble average. Partial rigorous support for 2-D analogs of Kolmogorov's 3-D dissipation law, as well as the power law for the distribution of energy are given.

Keywords:

Mathematics Subject Classification: 35Q30, 76F02.

Citation:

Article Metrics

HTML views() PDF downloads(88) Cited by(0)

On universal relations in 2-D turbulence

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

On universal relations in 2-D turbulence

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content