Influence of a wavy boundary on turbulence.

Abstract

A previous paper from this laboratory presented measurements of turbulence that were made for water flowing over a wavy wall. The system was a 50 mm×600 mm rectangular channel for which the top wall was flat and the bottom wall was a train of sinusoidal waves with a wave length of 5 mm and a wave height of 0.50 mm. The Reynolds number, defined with the bulk velocity and the half-height of the channel, was 46,000. These conditions were such that a sand covered surface would be fully rough and characterized with a dimensionless sand roughness of k _s ⁺=104. The present paper presents measurements with Reynolds numbers of 11,000 and 3,200 for which the surface corresponds to the intermediate regime (k _s ⁺=22.4) and the hydraulically smooth regime (k _s ⁺=6.89). The measurements in the outer flow for k _s ⁺=22.4 differ from what is observed for k _s ⁺=104 in that the quadrant analysis of the Reynolds stress and the skewness coefficients for u _i and v _i are the same as found for flow over a flat boundary. Measurements of mean velocities, wall drag and turbulent intensities for k _s ⁺=6.89 are consistent with defining this surface as hydraulically smooth. Surprisingly the quadrant analysis of the Reynolds stress and measurements of the skewness factor for normal velocity fluctuations for k _s ⁺=6.89 are different from what is found for a flat surface. The contributions of quadrants 2 and 4 and their ratio are larger than what is found for a flat surface. Measurements for all three surfaces show smaller relative contributions for large wavenumber fluctuations. However, this is much more pronounced for k _s ⁺=6.89 and k _s ⁺=22.4.