LAGRANGIAN FIELD-THEORY, MULTIFRACTALS, AND UNIVERSAL SCALING IN TURBULENCE

We demonstrate that there is a complete analogy between multifractal scaling behavior in certain Lagrangian field theories and the scaling properties of inertial-range velocity fields in the common ''cascade models'' of turbulence. On this basis, we propose a renormalization group strategy to study the zero-viscosity limit of fully developed turbulence and establish its short-distance scaling properties. If these properties are due to an RG fixed point which is a universal ultraviolet attractor, then predicted consequences are exact relations between inertial and dissipation-range scaling exponents.