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arXiv · 1411.5764

On energy cascades in non-homogeneous 3D Navier-Stokes equations

R. Dascaliuc·Z. Grujić
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Abstract

We show - in the framework of physical scales and $(K_1,K_2)$-averages - that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale are sufficient to guarantee energy cascades in the forced Navier-Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws - in terms of Grashof number - for kinetic energy, energy flux, and energy dissipation rate. These are used to improve our sufficient condition for forced cascades in physical scales.

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R. Dascaliuc, Z. Grujić. 2014-11-21. On energy cascades in non-homogeneous 3D Navier-Stokes equations. https://arxiv.org/abs/1411.5764

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