Observations of the vertical structure of turbulent oscillatory boundary layers above fixed roughness using a prototype wideband coherent Doppler profiler: 2. Turbulence and stress

Abstract

Measurements of turbulence and shear stress in oscillatory boundary layers are reported from experiments carried out with a prototype wideband coherent Doppler profiler above fixed roughness beds of 0.37 mm diameter sand and 3.9 mm diameter gravel. The 10 s oscillation period and 0.75 m to 1.5 m oscillation excursions correspond to roughness Reynolds numbers for the gravel bed in the 290 to 490 range, assuring fully rough turbulent conditions. Bottom stress was estimated via the law-of-the-wall, the vertical integral of the defect acceleration, and the Reynolds stress. The Reynolds stress was obtained from the second moment of the beam-coordinate velocities. Bed friction factors, f w, from the defect stresses are in reasonable agreement with predictions based on Swart's empirical relation as modified by Nielsen (1992) and with values determined using Laser Doppler Anemometry (LDA) by Sleath (1987) via the defect method and by Jensen (1988) via the law-of-the-wall. The f w values determined here from the law-of-the-wall are higher than predicted (ca. 50% higher for the gravel bed), likely due to background vertical shear associated with residual motions in the tank. The Reynolds stresses are lower than the predictions by a factor of 3 to 4, compared to the factor of 5 to 10 obtained by Sleath (1987). Beam coordinate turbulent kinetic energy spectra indicate that the vertical momentum flux is mostly associated with fluctuations between the forcing frequency and the inertial subrange, the latter contributing typically less than 10% of the total observed Reynolds stress. Copyright 2012 by the American Geophysical Union.