Multi-affine model for the velocity distribution in fully turbulent flows

Abstract

A simple multi-affine model for the velocity distribution in fully developed turbulent flows is introduced to capture the essential features of the underlying geometry of the velocity field. We show that in this model the various relevant quantities characterizing different aspects of turbulence can be readily calculated A simultaneous good agreement is found with the available exprimental data for the velocity structure functions, the Dq spectra obtained from studies of the velocity derivatives, and the exponent describing the scaling of the spectrum of the kinetic energy fluctuations. Our results are obtained analytically assuming a single free parameter. The fractal dimension of the region where the dominating contribution to dissipation comes from is estimated to be D=2.88.