HIDDEN CONSERVATION-LAWS IN HYDRODYNAMICS - ENERGY AND DISSIPATION RATE FLUCTUATION SPECTRA IN STRONG TURBULENCE

The Hamiltonian formulation of hydrodynamics in Clebsch variables is u sed for construction of a statistical theory of turbulence. The statis tics of the Clebsch field is assumed to be close to Gaussian. It is sh own that the energy spectrum consists of two ranges with E(k) almost-e qual-to k-5/3 and E(k) almost-equal-to k-1. The spectrum of the dissip ation rate fluctuations has three scaling regimes: E(epsilon)(k) almos t-equal-to k-1; k-1/3 and k0 at the large, intermediate and small scal es, respectively. The origin of the exponential distribution of veloci ty differences is discussed. The new scaling regime corresponds to a h idden conservation law, discovered in the Clebsch formulation of hydro dynamics. It is shown that viscous effects are responsible for product ion of the conserved quantity. The theoretical predictions are compare d with results of numerical simulations of decaying turbulence.