Lagrangian and Eulerian Velocity Structure Functions in Hydrodynamic Turbulence

Abstract

The Lagrangian and Eulerian transverse velocity structure functions of fully developed fluid turbulence are found based on the inviscid Navier-Stokes equation. The structure functions are shown to obey the scaling relations S(n)(L)(tau) proportional to tau(xi(n)) and S(n)(E)(l) proportional to l(zeta(n)) inside the inertial range. The scaling exponents zeta(n) and xi(n) are calculated analytically without using dimensional considerations. This result is a significant step toward understanding the nature of hydrodynamic turbulence. The obtained values are in agreement with recent numerical and experimental data.