Probability density function and plus and minus structure functions in a turbulent channel flow

We consider the statistical properties of the longitudinal velocity increments in a turbulent channel flow at different distances from the wall. The probability density function (PDF) of the velocity difference of the streamwise component near the wall are found to be, especially at small scales, strongly skewed, showing a very long left tail. We consider plus and minus structure:functions and compute separately the statistics for the right and left part of the PDF. It is found that the relative scaling exponents for the right tail are less affected by the presence of the wall and their values are consistent with the;ones found in experiments in homogeneous and isotropic turbulence. A simple phenomenological model that explains the results obtained is also given.