Theoretical model for the Kramers-Moyal description of turbulence cascades

We derive the Kramers-Moyal equation for the conditional probability densit y of velocity increments from the theoretical model recently proposed by V. Yakhot [Phys. Rev. E 57, 1737 (1998)] in the limit of the high Reynolds nu mber. We show that the higher order (n greater than or equal to 3) Kramers- Moyal coefficients tend to zero and the velocity increments are evolved by the Fokker-Planck operator. Our results are compatible with the phenomenolo gical description, developed for explaining recent experiments by R. Friedr ich and J. Peinke [Phys. Rev. Lett. 78, 863 (1997)].