Propagation dynamics of diffusive pollutants on the water surface and in the water

Abstract

Firstly, the 2D problem of propagation of diffusing pollutant on the water surface is analyzed. Such model may be used, for example, to study the lifetime of the toxic pollutant spot on the water surface. For isotropic medium the boundary value problem for the diffusion equation is considered, the analytical solution of which may be obtained by means of Fourier method with consequent expansion of the arbitrary function in Bessel functions. The found analytical solution is compared with numerical solutions of the boundary value problem obtained with Mathematica software packages. The dependence in time of the pollution spot size is studied and the effect of geometrical and physical parameters on the pollution spot radius is discussed. Also the 3D problem of toxic pollutant propagation set on the flat bottom is examined. The size of the domain, where the concentration of the toxic pollutant is higher than the maximum permissible concentration, and the dynamics of this domain are studied. Refs 12. Figs 5.

Keywords:

diffusing pollutant, diffusion equation, toxic pollutant spot