A Langevin equation for turbulent velocity increments | Zendy

Philippe Marcq | Zendy; Antoine Naert | Zendy

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A Langevin equation for turbulent velocity increments

Author(s) -

Philippe Marcq,

Antoine Naert

Publication year - 2001

Publication title -

physics of fluids

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.188

H-Index - 180

eISSN - 1089-7666

pISSN - 1070-6631

DOI - 10.1063/1.1386937

Subject(s) - physics , langevin equation , turbulence , statistical physics , moment (physics) , stochastic process , gaussian , fokker–planck equation , classical mechanics , scale (ratio) , correlation function (quantum field theory) , length scale , probability density function , mechanics , differential equation , statistics , quantum mechanics , mathematics , dielectric

International audienceRecently, Friedrich and Peinke demonstrated empirically that a Fokker–Planck equation describesthe scale dependence of probability distribution functions of longitudinal velocity increments vr infully developed turbulent flows. Thanks to the analysis of an experimental velocity signal, thestochastic process vr is further investigated by examining the related Langevin equation. Thisprocess is found to be Markovian in scale because the turbulent velocity field is correlated overdistances much larger than the correlation length r of its spatial derivative. A Gaussianapproximation for the random force yields evolution equations for the structure functions ^vrn&.Analytic solutions are obtained, in agreement with experimental data for even-order moments whenthe scale r is larger than a few times r. The third-order moment ^vr3& is found linear in r, as predictedby Kolmogorov’s four-fifths law

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