Physical Review Letters · 1997 · 378 citations · 6 references
Turbulent CascadeMultiscale HydrodynamicsEngineeringPhysicsEnergy CascadeEntropyFluid MechanicsHydrodynamicsTurbulence ModelingTurbulenceStochastic ProcessesConditional Probability DistributionTurbulent Free JetTurbulent Flow Heat TransferProbability TheoryBrownian MotionJoint Probability DistributionHydrodynamic Stability
Turbulent free jets exhibit cascades of velocity fluctuations described by Kolmogorov–Oboukhov log‑normal models, forming the theoretical backdrop for this study. The authors compute the joint probability distribution of velocity increments at two scales from experimental jet data and formulate a stochastic process based on the Kolmogorov–Oboukhov log‑normal model. Experimental results show that the conditional distribution of velocity increments satisfies a Fokker‑Planck equation, with drift and diffusion coefficients linked to universal scaling and turbulence intermittency.
From experimental data of a turbulent free jet we calculate the joint probability distribution $p({v}_{1}{,L}_{1}{;v}_{2}{,L}_{2})$ for two velocity increments ${v}_{1}{,v}_{2}$ of different length scales ${L}_{1}{,L}_{2}$. We present experimental evidence that the conditional probability distribution $p({v}_{2}{,L}_{2}|{v}_{1}{,L}_{1})$ obeys a Fokker-Planck equation. We calculate the corresponding drift and diffusion coefficients and discuss their relationship to universal behavior in the scaling region and to intermittency of the turbulent cascade. We explicitly present a stochastic process for the log-normal model of Kolmogorov and Oboukhov [A. M. Oboukhov, J. Fluid Mech. 13, 77 (1962); A. N. Kolmogorov, J. Fluid Mech. 13, 82 (1962)].
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A. Tsinober · European Journal of Mechanics - B/Fluids · 1998 · 3.6K citations
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R. Friedrich, Joachim Peinke · Physica D Nonlinear Phenomena · 1997 · 97 citations