Rouse revisited: The bottom boundary condition for suspended sediment profiles

A linearly depth-dependent diffusivity is commonly used to model the vertical distribution of dilute, near-bed, suspended sediment in marine fluid environments, i.e., the Rouse model; this simplified form predicts unfortunately infinite concentration at the bed. That singularity causes problems in linking bed models to suspended sediment models. A common remedy to this problem is to assume a reference concentration and height above the bed, but some studies point to the arbitrariness of that procedure and suggest, instead, the existence of a residual eddy diffusion near the bed, which removes the singularity. In these past studies, the residual diffusion, epsilon(o), has been assigned a value based on the Nikuradse roughness height, k(s) = 2.5d(s), where d(s) is the (mean) equivalent sand-grain diameter. We examine this assumption by fitting a residual diffusion model to 14 time-averaged suspended-sediment profiles available in the literature, without assuming the Nikuradse length. This procedure produces epsilon(o) values from 0.6 to 13 cm(2) s(-1), which are much greater than both the (molecular) kinematic viscosity of water and the expected Brownian diffusion coefficient of the sediment grains of the reported sizes. These residual diffusion coefficients indicate mixing scale heights at the bed, epsilon(o)/kappa u(*), where kappa is von Karman's constant and u(*) is the shear velocity, are 7.4-56.0 x greater than the Nikuradse height, k(s). Although defined by only limited data, we also find that the residual diffusion correlates with grain size and the roughness Reynolds number but not with the Rouse parameter, nor with the shear and settling velocities. In addition, the residual diffusion coefficient correlates with van Ftijn's roughness scale, again based on the same limited data, suggesting that bedforms influence residual diffusion near the bed.