Vortex filament model and multifractal conjecture

Abstract

We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended self-similarity approach. The results obtained are shown to be in very good agreement with numerical simulations and experimental data. The role of more general stochastic solutions of the Navier-Stokes equation is discussed.