Statistical properties of a turbulent cascade. (English) Zbl 0897.76042
Summary: Statistical properties of a turbulent cascade are evaluated by considering the joint probability distribution \(p(\upsilon_1, L_1;\upsilon_2,L_2)\) for two velocity increments \(\upsilon_1,\upsilon_2\) of different length scales \(L_1,L_2\). We present experimental evidence that the conditional probability distribution \(p(\upsilon_2,L_2|\upsilon_1,L_1)\) obeys a Chapman-Kolmogorov equation. We evaluate the Kramers-Moyal coefficients and show evidence that higher-order coefficients vanish except for the drift and diffusion coefficient. As a result, the joint probability distributions obeys the Fokker-Planck equation. We calculate drift and diffusion coefficients and discuss their relationship to universal behaviour in the scaling region and to intermittency of the turbulent cascade.
MSC:
| 76F99 | Turbulence |
Keywords:
joint probability distribution; conditional probability distribution; Chapman-Kolmogorov equation; Kramers-Moyal coefficients; diffusion coefficient; Fokker-Planck equation; drift coefficientReferences:
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