Dispersion of conservative impurities in rivers: implications for compliance with environmental standards

Abstract

The research goal is to understand the mechanisms of transport and transformation of conservative impurities in river flows and provide practical solutions to ensure compliance with environmental standards. The need to close the system of equations and make it suitable for solving practical problems caused the addition of equations of motion with empirical regularities. We use an approach based on fundamental equations of hydrodynamics. The main task of mathematical transformations of the fundamental equations was: a) considering the variability of the turbulent exchange coefficients along the flow cross-section. b) addition of the obtained equations with empirical regularities linking the flow characteristics with the turbulent exchange coefficients. c) mathematical transformations were performed to obtain a group of closed equations for which approximate solution methods are known and developed. The best empirical regularities in determining the turbulent exchange coefficients were selected by applying a closed mathematical model. For each desired variable, we obtained an equation of the evolutionary type, which lends itself well to algorithmization. The schemes presented in the article allow us to design computational algorithms using classical approaches to solving impurity transfer equations with variable coefficients of turbulent exchange.