Modelagem matemática do escoamento médio do ar para áreas de floresta da Amazônia

Abstract

Due to the vast expanse of the Amazon rainforest and its interaction with atmospheric atmospheric runoff, a mathematical modeling study was carried out that the type of vertical distribution of plant matter with this runoff. Specifically, two models were considered: one with a leaf area density constant with height, called “rectangular”, and another with linear variation of this density, increasing between ground level and a point of greater concentration of concentration, 𝑧𝑚, and decreasing between 𝑧𝑚 and the top of the forest, called “triangular”. These biomass models were applied to the Navier-Stokes equation, structuring a term that expresses the drag force between the foliage and the air, to obtain a mathematical description of the stationary flow in areas of forest areas of the Amazon. By carrying out tests with variations in the input parameters of the models obtained, it was found to be more sensitive to air viscosity, horizontal pressure variation and the term that expresses the rate of the rate of absorption of the quantity of movement of the flow. The results of application of the mathematical models developed for a forest area in the Amazon forest area, showed good correspondence with the wind speed profiles generated with data collected in the Uatumã Sustainable Development Reserve. The results of application of the mathematical models developed for a forest area in the Amazon forest area, showed good correspondence with the wind speed profiles generated with data collected in the Uatumã Sustainable Development Reserve. Uatumã Sustainable Development Reserve, with coefficients of determination (𝑅 2) for the dry and rainy seasons, equal to 0.981 and 0.989, respectively. It can therefore be concluded that the triangular model, despite including more variables in its design and requiring more effort to obtain to obtain solutions to the differential equations that describe it, presents slightly smaller approximations to the observational data than the rectangular model. model, which is simpler and less laborious to obtain and apply. KEYWORDS: Mathematical Modeling; Air Flow; Amazon.