Environmental Science & Technology, es060438k (2006) Modeling the Transport and Inactivation of E. coli and Enterococci in the Near-Shore Region of Lake Michigan

where 2S is the viscosity computed by the Smagorinsky formulation (Smagorinsky, 1963), α is a constant in the range 0.01-0.5 and A denotes the area of the current element. A value of α = 0.1 was used keeping in mind the fine resolution of the mesh. Similar to the eddy viscosity, turbulent diffusion in the transport equations (equation 4 in the paper) represents all those processes that can not be explicitly resolved by the computational grid. Turbulent diffusion values are usually estimated using either scale arguments and empirial relations (e.g., Richardson’s 4/3 power law) or from dye diffusion studies conducted in the near-shore region. Based on dye studies, Inman et al. (1971) reported turbulent diffusion values in the range 2.0 to 5.9 m/s for Scripps Beach in California. We used a constant diffusion coefficeint of 2 m/s in the near-shore region but values in the range 2 to 10 m/s produced similar results. Since our hydrodynamic and transport models used the same computational grid, we used the same values for both eddy viscosity and turbulent diffusion in the near-shore region (Holland et al., 2003). In the offshore region, eddy diffusion values in our model changed with grid size and velocity as shown below.