Probability distribution functions and coherent structures in a turbulent channel

Abstract
With the aid of a direct numerical simulation of an incompressible plane turbulent channel at h+=162, we have determined the probability distribution functions (PDF’s) of pressure and of the various velocity components from the wall to the channel center. The pressure turns out to be symmetric with exponential tails at the wall as well as at y+=2.5. At y+=12, where the streamwise streaks intensity is maximum, the pressure has become asymmetric. This character intensifies with the distance away from the wall and the distribution obtained in the channel center resembles those determined in isotropic turbulence and free-shear flows. Very close to the wall (y+=2.5), the PDF of u is highly skewed, with exponential and sub-Gaussian distributions at high and low values, respectively. This indicates that the high-speed streaks are very intermittent at the wall. The reverse occurs close to the channel center, where intense negative u prevail. Then we show that the most probable orientation of the fluctuating vorticity vector is perpendicular to the wall in the region 5<y+<30 (which is basically in the low- and high-speed regions), while it is 45° with respect to the wall above.