On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows |
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Authors: | R Dascaliuc C Foias MS Jolly |
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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 |
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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 and respectively, where 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. |
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Keywords: | 47 27 |
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