On the vertical and temporal structure of flow and stress within the turbulent oscillatory boundary layer above evolving sand ripples

Abstract The vertical structure of flow and stress within turbulent oscillatory boundary layers above evolving sand ripples is investigated in experiments carried out using a prototype wide-band coherent Doppler profiler in an oscillating boundary facility with beds of 0.216 mm median diameter sand, 10 s oscillation period, and 0.9 m excursion (Shields parameter=0.11). The bed evolved from an initial nominally flat state through 5 cm wavelength, nearly two-dimensional ripples to 12 cm wavelength, three-dimensional ripples. Average ripple height increased from 0.2 cm to 1.4 cm, corresponding to roughness Reynolds numbers between 68 and 7700. Average ripple steepness increased from 0.03 to 0.15. Bed elevation spectra exhibit the shift towards lower spatial frequencies observed by Davis et al. (2004) and, at higher spatial frequencies, a saturation range analogous to that in surface gravity wave spectra. Horizontal velocity profiles exhibit the phase lead and overshoot expected for oscillatory boundary layer flow. Bottom stress estimates are obtained from the acceleration defect, the Reynolds stress and the law-of-the-wall. The defect stress estimates are bounded above and below by the Reynolds stress and the law-of-the-wall estimates, respectively. The values of the bottom friction coefficient and hydraulic roughness from the defect stress estimates are consistent with results from previous work on equilibrium orbital-scale ripples, as summarized by Nielsen (1992) , indicating that ripple evolution was quasi-steady.