Effect of initial conditions on the dispersion dynamics of a diffusing substance

Abstract

This work continues the studies on the diffusion of a substance over a water surface, in particular, the effect of nonuniformity in the initial distribution of a substance on the dynamic characteristics of a pollution spot has been investigated. A pollution spot is understood to mean a water surface area in which the concentration of a diffusing substance is higher than a specified threshold value. The analytical solutions of boundary-value problems have been found by the Fourier method in special functions for the equation of diffusion in unlimited areas. Asymptotic and numerical methods are used for their analysis. It has been concluded that the initial distribution of a polluting substance over the surface has a slight effect not only on the lifetime of a pollution spot but also on its maximum radius at the same volume of pollution. The maximum size of a pollution spot and the time moment at which this size is attained have been found in the case of a uniform substance distribution.