Flow patterns near shore are complex, depending on meteorological conditions, bathymetry, and boundary conditions. The nonlinear interactions of waves, current, and the discharge of polluted fluids from factories or domestic sewage can be quite complex. As flow velocity increases, laminar flows will yield to turbulent flows. Turbulent eddies of both small and large scales will evolve. The scale of eddies is the distance over which the eddy velocity varies appreciably. The function inside the integral actually represents a normal distribution in probability theory or the Gaussian normal distribution. This integral relates to the error estimation in probability theory, the theory of heat conduction, fluid pressure in a porous medium, and the Rayleigh impulsive flow problem. The change in the concentration of pollutants in water can come from two mechanisms; the first is mechanical mixing of fluids due to a flowing motion of the fluid, and the second is of diffusion type due to turbulent eddies.