PROBABILITY DENSITY AND SCALING EXPONENTS OF THE MOMENTS OF LONGITUDINAL VELOCITY DIFFERENCE IN STRONG TURBULENCE

We consider a few cases of homogeneous and isotropic turbulence differ ing by the mechanisms of turbulence generation. The advective terms in the Navier-Stokes and Burgers equations are similar. It is proposed t hat the longitudinal structure functions S-n(r) in homogeneous and iso tropic three-dimensional turbulence are governed by a one-dimensional (1D) equation of motion, resembling the 1D Burgers equation, with the strongly nonlocal pressure contributions accounted for by Galilean inv ariance-breaking terms. The resulting equations, not involving paramet ers taken from experimental data, give both scaling exponents and ampl itudes of the structure functions in an excellent agreement with exper imental data. The derived probability density function P(Delta u,r)not equal P(-Delta u,r), but P(Delta u,r)=P(-Delta u,-r), in accord with the symmetry properties of the Navier-Stokes equations. With decrease of the displacement r, the probability density, which cannot be repres ented in a scale-invariant form, shows smooth variation from the Gauss ian at the large scales to close-to-exponential function, thus demonst rating onset of small-scale intermittency. It is shown that accounting for the subdominant contributions to the structure functions S-n(r)pr oportional to r(xi n) is crucial for a derivation of the amplitudes of the moments of the velocity difference.