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Cascade of energy in turbulent flows. (English. Abridged French version) Zbl 0986.35089
From the summary: A starting point for the conventional theory of turbulence is the notion that, on average, kinetic energy is transferred from low wave number modes to high wave number modes. Such a transfer of energy occurs in a spectral range beyond that of injection of energy, and it underlies the so-called cascade of energy, a fundamental mechanism used to explain the Kolmogorov spectrum in three-dimensional turbulent flows. The aim of this note is to prove this transfer of energy to higher modes in a mathematically rigorous manner, by working directly with the Navier-Stokes equations and stationary statistical solutions obtained through time averages.

MSC:
35Q35 PDEs in connection with fluid mechanics
76F55 Statistical turbulence modeling
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