Structure Functions in a wall-turbulent shear flow

Wavelet and quadrant analyses were applied to turbulent velocity data in order to investigate the transition from the anisotropy of energy- containing eddies to the isotropy of the inertial subrange scales. The quadrant analysis of the wavelet coefficients of longitudinal and vertical velocity components allows the evaluation of the velocity structure functions and the momentum cospectrum as a function of the separation distance and of the quadrants. In an isotropic condition the contribution both of ejections and sweeps (even quadrants) and both of reflections and deflections (odd quadrants) has to be equal. The performed analysis has shown that in neutrally stratified conditions the transition to isotropy occurs in a frequency range (0.2 < r/z < 3) usually referred to as internal to the inertial subrange. In the transition region, as in the isotropic region, the velocity structure functions still agree with the 1941 and 1962 Kolmogorov theories; but on the other hand the structure functions of the even and odd quadrants are fitted by power laws of different slopes in the transition region. The proposed analysis allows the investigation within the transition region of the different dynamical structure in the energy transfer from the energy-containing scales to the isotropic scales.