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

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

Proceedings of the Royal Society of Edinburgh Section A, Volume 149, Issue 2 April 2019 , pp. 429-446 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-dimen...

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description Proceedings of the Royal Society of Edinburgh Section A, Volume 149, Issue 2 April 2019 , pp. 429-446 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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A determining wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes equations, is a mathematical analog of Kolmogorov's number. 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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.</abstract><doi>10.48550/arxiv.1510.00379</doi><oa>free_for_read</oa></addata></record>
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title Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
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