TEMPORAL MULTISCALING IN HYDRODYNAMIC TURBULENCE

On the basis of the Navier-Stokes equations, we develop the high Reyno lds number statistical theory of different-time, many-point spatial co rrelation functions of velocity differences, We find that their time d ependence is not scale invariant: n-order correlation functions exhibi t infinitely many distinct decorrelation times that are characterized by anomalous dynamical scaling exponents. We derive exact scaling rela tions that bridge all these dynamical exponents to the static anomalou s exponents zeta(q) of the standard structure functions. We propose a representation of the time dependence using the Legendre-transform for malism of multifractals that automatically reproduces all the newly fo und bridge relationships.