Analysis of energy cascade models of turbulence

The exponent tau(p) that describes the scaling of the order-p moment of the energy dissipation field in fully developed turbulence is studied in a range which extends to negative values of p. The curve tau(p) vs p and its derivative tau(')(p) are estimated in various ways, including a two-scale method. Predictions of recent cascade models agree with our findings, within the statistical errors, for moderately large, positive p. Evident discrepancies already appear, however, in the interval pin[0,1], and sometimes become dramatic for p<0. In the discussion of a class of cascade models, we present a scaling law which relates different moments to one another.