Cascade Processes and Fully Developed Turbulence.

The energy cascade process in turbulent flows is studied. Kolmogorov inertial range theories are critically reviewed and the multifractal characterization is discussed. Multiplicative cascade models are compared to the energy dissipation field (EDF) measured in the atmosphere. Landau's objection to the 1941 Kolmogorov theory is extended to the predictions of statistical fluid mechanics. The hypothesis Delta v(lambda L) {buildrel {d}over=} lambda^ {1/3} Delta v(L) is rejected with a statistical test. The moments <( logvarepsilon(L))^{p}>, where varepsilon(L) denotes the EDF averaged over a volume of size L, are shown to be gaussian. For the EDF: Convergence tests showed that the exponents tau(q) were not reliable for q < 0; the correlations obey <(mu_{x}(delta)) ^{p}(mu_{x+delta }(delta))^{q}> ~ delta^{gamma(p,q)} but gamma does not always equal the value obtained with a multinomial measure; a privileged scale ration r ~ 1/2 is suggested by the prefactor oscillations of the correlation function. The implications of these results for the modelling of the EDF are discussed.