LARGE-SCALE COHERENCE AND ANOMALOUS SCALING OF HIGH-ORDER MOMENTS OF VELOCITY DIFFERENCES IN STRONG TURBULENCE

The Hamiltonian formulation of hydrodynamics in Clebsch variables is u sed for construction of a statistical theory of turbulence. It is show n that the interaction of the random and large-scale coherent componen ts of the Clebsch fields is responsible for generation of two energy s pectra E (k) is-proportional k-7/3 and E(k) is-proportional-to k-2 at scales somewhat larger than those corresponding to the -5/3 inertial r ange. This interaction is also responsible for the experimentally obse rved Gaussian statistics of the velocity differences at large scales, and the nontrivial scaling behavior of their high-order moments for in ertial-range values of the displacement r. The ''anomalous scaling exp onents'' are derived and compared with experimental data.