Application of mathematical modeling for water environment problems

Abstract

Viatcheslav Solbakov käsittelee väitöstutkimuksessaan saasteiden leviämisen laskentaa luonnonvesissä. Tässä virtauksilla ja aineiden turbulenttisella sekoittumisella on keskeinen merkitys. Solbakov vertaili erilaisia turbulenssin matemaattisia kuvauksia ja niiden vaikutusta leviämislaskennan tarkkuuteen. Hän kehitti erityisesti aiempaa tarkempia menetelmiä erikseen sekä satunnaispäästön ja toisaalta jatkuvan päästön sekoittumisen laskentaa varten. Näitä menetelmiä hän sitten käytti kiintoaineen leviämisen laskennassa. Mallin runkona hänellä oli tunnettu hydrodynaaminen ”Princton Ocen Model (POM)”-malli joka on vapaasti saatavilla ja jota käytetään erittäin paljon ympäri maailmaa erilaisten virtausten laskemiseen.

In the first part of the thesis we present a thorough analysis of pollutant dispersion in water environment and physical mechanisms of its turbulent dispersion in water. While analyzing two turbulent diffusion models we find analytically that the Richardson model with variable coefficients is substantially better in comparison with constant coefficients. Also we are interested in modeling of shot and continuous intrusion of contaminants. For the 2D transport and diffusion equation with homogeneous coefficients we manage to construct analytical solution both for shot and continuous intervention cases. The latter case is treated via a specially devised “cloud method”. This method enables to account for the turbulence and “4/3” law which seems to be new for the case of continuous intervention. The method is expanded to the case of suspended solids dispersion. The case of 3D transport and diffusion equation is also considered. The solution method based on Gaussian clouds is applied to 3D transport and diffusion of sediment substances. The numerical method based on momentum approach is used for the definition of the cloud parameters. The way to introduce the “4/3” law for the 3D transport and diffusion equation in the case of substances sedimented on the bottom is also given. The approach of implementation of connection of near field and far field regions is considered. In the second part of the thesis the task of calculations of hydrodynamics parameters (sea level, current velocity and temperature distribution) is formulated for various environments based on 3D geophysical hydrodynamics equations. Special emphasis made on the circumstance that opens boundary conditions must be compatible both for the 3D and for the shallow water formulation. For a numerical solution of the three-dimensional nonstationary equations of geophysical hydrodynamics we use finite-difference equations which conserve the main variables (water and heat) and take into account the timedependence variability of the solution area. Some illustrations and simulation results are represented for various pools and different environment conditions. The results of simulations for a short-term variability of circulation and thermal structure in Lake Jyväsjärvi are presented. Common problems arising while designing information systems are examined from the point of view of joined operation of mathematical models, data bases and Geographic information system. The problems considered here are of interest for both academic and practical applications in the field of environment modeling.