A unified framework for bed shear stress and boundary layer thickness for rough and smooth beds in bare and vegetated channels

Bed shear stress is a key parameter governing sediment transport and fluxes at the sediment–water interface. In vegetated channels, predicting bed shear stress, especially for rough beds, remains a challenge. This study developed a unified theoretical model for bed shear stress that smoothly spans conditions from bare bed to vegetated bed for both smooth and rough beds. Building on phenomenological turbulence theory, the model relates bed shear stress to the characteristic velocities of the larger energy-containing eddies and the smaller, near-bed eddies, with the new assumption that the bottom boundary layer (BBL) thickness controls the larger, energy-containing eddy length scale. The BBL was defined as the region within which the bed shear stress contributed significantly, compared to vegetation drag, and a force balance predicted that the BBL thickness scales with the ratio of bed shear stress to vegetation drag. In the limit of zero vegetation density, the BBL thickness equals the water depth, and the bed shear stress model reduces to the classical bare bed formulation. With increasing vegetation density (drag), the thickness of the boundary layer decreases, and the bed friction coefficient increases, which is consistent with previous observations. For rough beds, the bed friction coefficient increases with bed roughness, but is not dependent on the mean velocity. In contrast, for smooth beds, the bed friction coefficient decreases with increasing mean velocity. The coupled models for bed shear stress and BBL thickness were compared against 114 physical and numerical experiments from multiple previous studies.