Effect of the initial conditions on dispersion dynamics of pollution spots

Abstract

Current research results on processes of diffusion of a substance on the water surface are reported. In particular, the influence of initial distribution unevenness of the diffusing substance on dynamic characteristics of the pollution spot is studied. The pollution spot is a domain of the surface, in which the concentration of the diffusing substance is greater than a certain value. Using Fourier’s method analytical solutions of boundary value problems for the diffusion equation are found in special functions in unbounded domains. For their analysis asymptotic and numerical methods are used. It has been proved that at identical volumes of pollution its initial distribution on a surface has weak impact not only on the spot’s lifetime, but also on its maximum radius. In case of uniform distribution of the substance the maximum size of the pollution spot and the timepoint when it is reached are found. Refs 7. Figs 3. Table 1.