Since many pollutants enter lakes (and other water-bodies for that matter) at their periph...

Since many pollutants enter lakes (and other water-bodies for that matter) at their peripheries, an important water-quality problem involves modeling the distribution of contaminants in the vicinity of a waste discharge or a river. For a vertically well-mixed, constant-depth layer, the steady-state distribution of a pollutant reacting with first-order decay is represented by

where the x and y axes are defined to be parallel and perpendicular to the shoreline, respectively (Fig. P7.45). The parameters and variables are: U_x = the water velocity along the shoreline (m/d), c = concentration, E = the turbulent diffusion coefficient, and k = the first-order decay rate. For the case where a constant loading, W, enters at (0, 0), the solution for the concentration at any coordinate is given by

where

where Y = the width, H = depth, and K₀ = the modified Bessel function of the second kind. Develop a MATLAB script to generate a contour plot of concentration for a section of a lake with Y = 4.8 km and a length from X = –2.4 to 2.4 km using Δx = Δy = 0.32 km. Employ the following parameters for your calculation: W = 1.2 × 10¹², H = 20, E = 5 × 10⁶, U_x = 5 × 10³, k = 1, and n = 3.

FIGURE P7.45: Plan view of a section of a lake with a point source ofpollutant entering at the middle of the lower boundary.