Velocity Pulse Model for Turbulent Diffusion from Flowing Water into a Sediment Bed

Abstract

The model simulates the transfer of turbulence from flowing water into a sediment bed, and its effect on the diffusional mass transfer of a solute e.g., oxygen, sulfate, or nitrate in the sediment bed. In the pulse model, turbulence above the sediment surface is described by sinusoidal variations of vertical velocity in time. It is shown that vertical velocity components dampen quickly inside the sediment when the frequency of velocity fluctuations is high and viscous dissipation is strong. Viscous dissipation inside the sediment is related to the apparent viscosity depending on the structure of the sediment pore space, i.e., the porosity and grain diameter, as well as inertial effects when the flow is turbulent. A value /0 between 1 and 20 0 is kinematic viscosity of water has been considered. Turbulence penetration into the sediment is parametrized by the Reynolds number Re= UL/ and the relative penetration velocity W / U, where Uamplitude of the velocity pulse; and Wpenetration velocity; L = WTwave length of the velocity pulse; and T is its period. Amplitudes of vertical velocity components inside the sediment and their autocorrelation functions are computed, and the results are used to estimate eddy viscosity inside the sediment pore system as a function of depth. Diffusivity in the sediment pore system is inferred by using turbulent or molecular Schmidt numbers. Turbulence penetration from flowing water can enhance the vertical diffusion coefficient in a sediment bed by an order of magnitude or more. Penetration depth of turbulence is higher for low frequency velocity pulses. Vertical diffusivity inside the pore system is shown to decrease more or less exponentially with depth below the sediment/water interface. Vertical diffusivities in a sediment bed estimated by the model can be used in pore water quality models to describe vertical transport from or into flowing surface water. The analysis has been conducted for a conservative material, but source and sink terms can be added to the vertical transport equation.