Reynolds stress distribution and turbulence generated secondary flow in the turbulent three-dimensional wall jet

The lateral half-width of the turbulent three-dimensional wall jet is typically five to eight times larger than the vertical half-width normal to the wall. Although the reason for this behaviour is not fully understood, it is caused by mean secondary flows that develop in the jet due to the presence of the wall. The origin of the secondary flow has been associated previously with both vorticity reorientation and also gradients in the Reynolds stresses, although this has not been directly quantified as yet. The present investigation focuses on a wall jet formed using a circular contoured nozzle with exit Reynolds number of 250 000. Stereoscopic particle image velocimetry measurements are used herein to measure the three-component velocity, thereby allowing access to the full Reynolds stress tensor that contributes to the secondary flow in a turbulent three-dimensional wall jet. Throughout the jet, the Reynolds normal stress ($\overline{u^{2}}$) makes the largest contribution to the Reynolds stress field whereas Reynolds shear stress ($\overline{vw}$) is found to be negligible when compared with other stresses. In particular, the differences in the Reynolds normal stresses ($\overline{v^{2}}-\overline{w^{2}}$) are found to be significantly larger than $\overline{vw}$; these terms are important for the generation of turbulence secondary flow in the wall jet. Above all, the differences in the Reynolds normal stresses are oriented to reinforce the near-wall streamwise vorticity, and thus contribute to the large lateral growth of this flow. The contours of the turbulent kinetic budget indicate that the turbulent energy budget obtained on the jet centreline is different from that obtained off of the jet centreline.