Modeling of Vertical Solute Dispersion in a Sediment Bed Enhanced by Wave‐Induced Interstitial Flow1

Abstract: Mass (solute) transport in a stream or lake sediment bed has a significant effect on chemical mass balances and microbial activities in the sediment. A “1D vertical dispersion model” is a useful tool to analyze or model solute transfer between river or lake water and a sediment bed. Under a motionless water column, solute transfer into and within the sediment bed is by molecular diffusion. However, surface waves or bed forms create periodic pressure waves along the sediment/water interface, which in turn induce flows in the pores of the sediment bed. The enhancement of solute transport by these interstitial periodic flows in the pores has been incorporated in a 1D depth‐dependent “enhanced dispersion coefficient (D_E).” Typically, D_E diminishes exponentially with depth in the sediment bed. Relationships have been developed to estimate D_E as a function of the characteristics of sediment (particle size, hydraulic conductivity, and porosity) and pressure waves (wave length and height). In this paper, we outline and illustrate the calculation of D_E as well as the penetration depth (d_p) of the flow effect. Sample applications to illustrate the computational procedure are provided for dissolved oxygen transfer into a stream gravel bed and release of phosphorus from a lake bed. The sensitivity of the results to input parameter values is illustrated, and compared with the errors obtained when interstitial flow is ignored. Maximum values of D_E near the sediment surface can be on the order of 1 cm²/s in a stream gravel bed with standing waves, and 0.001 cm²/s in a fine sand lake bed under progressive surface waves, much larger than molecular diffusion coefficients.