Time- and space-invariant parameterizations of the wave-bottom boundary layer over mobile rippled beds

Abstract:

The time-invariant form of the double-averaged Navier-Stokes equations was implemented on the nearbed velocity field over a rippled sediment bed. Data sets with relative roughness (A/k_n) ranging from 0.7 to 9.5 were analyzed to build a depiction of the different mechanisms responsible for transferring momentum into the bed. The analysis shows form stresses dominating the total small-scale stress for low relative roughness, and Reynolds stresses prevailing at higher relative roughness. The associated eddy viscosity estimates using the overall mean velocity as the velocity scale, agree with the model by Zedler and Street (2006), with a slight modification to their nearbed augmentation function. Bedform-induced pressure was estimated by solving the double-averaged momentum balance. Examination of its depth-dependent behavior indicates a close relationship with the presence of beform-induced coherent motions. Furthermore, comparisons between form drag estimates achieved from both, bedform-induced pressure and velocity-vorticity correlations, suggest a substantial role of coherent vortices in the depiction of the pressure field near bedforms.