Euler equations and turbulence: analytical approach to intermittency

Details Euler equations and turbulence: analytical approach to intermittency Euler equations and turbulence: analytical approach to intermittency

2012-02-07

arxiv.org/abs/1202.1460v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

In this note we introduce in precise mathematical terms some of the empirical concepts used to describe intermittency in a fully developed turbulence. We will give definitions of the active turbulent region, volume, eddies, energy dissipation set, and derive rigorously some power laws of turbulence. In particular, the formula for the Hausdorff dimension of the energy dissipation set will be justified, and upper/lower bounds on the energy spectrum will be obtained.

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