Statistical properties of a turbulent cascade

Statistical properties of a turbulent cascade are evaluated by considering 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 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 a 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.