DESCRIPTION OF A TURBULENT CASCADE BY A FOKKER-PLANCK EQUATION

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 incr ements v(1),v(2) of different length scales L(1),L(2). We present expe rimental evidence that the conditional probability distribution P(v(2) , L(2) \v(1), L(1)) obeys a Fokker-Planck equation. We calculate the c orresponding drift and diffusion coefficients and discuss their relati onship to universal behavior in the scaling region and to intermittenc y 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 (1 962)].