Ladder theorem and length-scale estimates for a Leray alpha model of turbulence

In this paper, we study the Modified Leray alpha model with periodic boundary conditions. We show that the regular solution satisfies a sequence of energy inequalities which are called “ladder inequalities”. Furthermore, we estimate some quantities of physical relevance in terms of the Reynolds number.

Keywords

turbulence models, regularity, Navier-Stokes equations

2010 Mathematics Subject Classification

35Q30, 76B03, 76D05, 76F05

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Published 21 December 2011