Journal of Fluid Mechanics

Structure of the Reynolds stress near the wall

W. W.  Willmarth a1 and S. S.  Lu a1
a1 Department of Aerospace Engineering, The University of Michigan

Article author query
willmarth ww   [Google Scholar] 
lu ss   [Google Scholar] 


Experimental studies of the flow field near the wall in a turbulent boundary layer using hot-wire probes are reported. Measurements of the product uv are studied using the technique of conditional sampling with a large digital computer to single out special events (bursting) when large contributions to turbulent energy and Reynolds stress occur. The criterion used to determine when the product uv is sampled is that the streamwise velocity at the edge of the sublayer should have attained a certain value. With this simple criterion we find that 60% of the contribution to $\overline{uv}$ is produced when the sublayer velocity is lower than the mean. This result is true at both low, Rθ = 4230, and high, Rθ = 38 000, Reynolds numbers. With a more strict sampling criterion, that the filtered sublayer velocity at two side-by-side points should be simultaneously low and decreasing, individual contributions to $\overline{uv}$ as large as 62 $\overline{uv}$ have been identified. Additional measurements using correlations between truncated u and v signals reveal that the largest contributions to the Reynolds stress and turbulent energy occur when u < 0, v > 0 during an intense bursting process and the remainder of the contributions occur during a less intense recovery process. Thus, contributions to the turbulent energy production and Reynolds stress at a point near the wall are of relatively large magnitude, short duration and occur intermittently. A rough measure of the intermittency factor for uv at a point near the wall is 0·55 since 99% of the contribution to $\overline{uv}$ is made during only 55% of the total time.

(Received December 13 1971)