Spatially averaged, vegetated, oscillatory boundary and shear layers

Oscillatory boundary layers over flat and rippled seabeds are well described in the literature. However, the presence of protruding vegetation stems has received no theoretical or experimental attention. The present work establishes an analytical constant viscosity model akin to the Stokes oscillatory boundary layer solution and a nonlinear varying-viscosity numerical model with a turbulence closure. The two models are used to describe the importance of vegetation and free stream velocity characteristics on spatially averaged oscillatory boundary layers: their friction factors, thickness and phase leads over the free-stream velocity. The models are periodic in time and resolve boundary and shear layers over the vertical, contrary to past efforts applying two-layer models. The models are extended to investigate the importance of finite wavelengths with steady streaming stresses and their associated mean velocity profile. Steady streaming is quantified both for the near-bottom streaming within the canopy and for the streaming in the shear layer above the canopy. Finally, akin to theoretical and experimental works on mean flows over unvegetated and flat seabeds due to oscillatory and nonlinear free-stream velocities, the numerical model investigates varying degree of nonlinearity for velocity- and acceleration-skewed velocity signals, and it is identified that the presence of vegetation stems gives rise to an additional contribution to the horizontal momentum balance which is not present for unvegetated conditions. Finally, it is discussed how the presence of a free surface, contrary to purely oscillatory conditions, alters the horizontal momentum balance within and above the canopy.