Mathematical modeling of the state of forest phytocenoses under natural and man-made disasters

Abstract

The man-induced stress in the biosphere in general and in forest phytocenoses in particular is steadily increasing. Forest fires are the most important consequence of the man-induced stress and of natural and industrial disasters. According to [1, 2], forest fires in Russia annually destroy on average up to 1 million ha of forests. It is therefore relevant to develop a general mathematical model of heat and mass transfer processes in forest phytocenoses for predicting their state under lower, upper, and massive forest fires [1, 2] with allowance for simultaneous heat and mass transfer between the forest phytocenosis and the ground layer of the atmosphere. The general mathematical model can be applied to develop simplified mathematical descriptions of various levels, appropriate data bases, and numerical solution procedures for problems of the theory of forest fires. This approach should enable us to estimate their accuracy by allowing for the omitted terms. In this article, we develop the results of [2, 3] and refine the general physico-mathematical model of lower, upper, and massive forest fires. We pose and solve numerically the problem of fire-center aerodynamics and the problem of repeated radioactive contamination of an area by fires in radioactive forests. We also consider the problem of massive forest fires as a result of industrial or natural disasters. The solution of the first problem produces the fields of velocities, temperatures, and radioactive aerosol concentrations at various time instants. Analysis of these fields shows that the zone of repeated radioactive contamination grows with the increase of wind velocity and the quantity of heat released by the forest fire. The solution of the second problem produces the fields of velocities, temperatures, and component concentrations. The ignition of forest combustibles has been analyzed and numerical estimates of the size of the ignition zone in the region of the Tunguska disaster have been obtained.