Hydrodynamic Turbulence Has Infinitely Many Anomalous Dynamical Exponents

Abstract

On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit $n-1$ distinct decorrelation times that are characterized by $n-1$ anomalous dynamical scaling exponents. We derive exact scaling relations that bridge all these dynamical exponents to the static anomalous exponents $ζ_n$ of the standard structure functions.