Reynolds stress and joint probability density distributions in the u-v plane of a turbulent channel flow

Abstract

The joint probability density distributions, p (u,v), of the u and v turbulence components are presented for nine positions across a fully developed turbulent channel flow. These distributions were determined by using 512 000 pairs of u and v values at each position and thus enable comparison of the relative character between the distributions. To show the contribution to the Reynolds stress, −ρ$\overline{\mathrm{uv}}$ at each point in the u‐v plane, the distributions of uv p (u,v) were determined. These distributions show the relative contributions to $\overline{\mathrm{uv}}$ as a function of position across the channel. Finally, the distributions of p (u,v) are compared with those of uv p (u,v). The most probable pairs of velocities do not produce the largest contribution to $\overline{\mathrm{uv}}$ .