Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations

Alexey Cheskidov; Mimi Dai

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arXiv · 1510.00379

Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations

Alexey Cheskidov·Mimi Dai

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Abstract

Kolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional fluid flow. A determining wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes equations, is a mathematical analog of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining wavenumber for the 3D Navier-Stokes equations whose time average is bounded by Kolmogorov's dissipation wavenumber for all solutions on the global attractor whose intermittency is not extreme.

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Alexey Cheskidov, Mimi Dai. 2019-07-19. Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations. https://arxiv.org/abs/1510.00379

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