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On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows
Authors:R Dascaliuc  C Foias  MS Jolly
Institution:a Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA
b Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
c Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
Abstract:Rigorous upper and lower bounds are proved for the Taylor and the Kolmogorov wavenumbers for the three-dimensional space periodic Navier-Stokes equations. Under the assumption that Kolmogorov’s two-thirds power law holds, the bounds sharpen to View the MathML source and View the MathML source respectively, where View the MathML source is the Grashof number. This provides a rigorous proof that the power law implies (1) the energy cascade, (2) Kolmogorov dissipation law, and (3) a connection between κT and κ?. The portion of phase space where a key a priori estimate on the nonlinear term is sharp is shown to be significant by means of a lower bound on any probability measure associated with an infinite-time average.
Keywords:47  27
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