Fokker-Planck equation for the energy cascade in turbulence
Résumé
We present a detailed analysis of the energy dissipation averaged over a distance r,e r , in terms of a
stochastic process through scales. Using experimental data recorded in a low temperature helium jet, we give
evidence that the probability density function of ln(e r) obeys a Fokker-Planck equation. The drift and diffusion
coefficients are calculated directly from the data. The drift is linear in ln(e r) and the diffusion is constant. With
these coefficients, the equation can be solved exactly, giving a Gaussian probability density function for ln(e r).
The mean and variance of this quantity are discussed in comparison with other log-normal models of intermittency.
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