16th International Northern Research Basins Symposium and Workshop Petrozavodsk, Russia, 27 Aug. ­ 2 Sept. 2007 Numerical analysis of migration and accumulation of pollutants near to bottom of water bodies Vladimir E. Putyrsky Institute of Water Problems of Russian Academy of Science, Gubkin, 3, Moscow, RUSSIA e-mail: putyrsky@aqua.laser.ru ABSTRACT Scientific and methodological problems are examined of the pollutant dispersion within inland water bodies and water courses by interaction between the fluxes at the divides of water, atmosphere and near-tobottom areas (Putyrsky, 1993). With the use of a semi-empirical turbulent diffusion equation, regularities in the pollutant area from technogenic sources were investigated with taken into account the sedimentation processes. Mathematical models have been developed for modeling the processes of accumulation of pollutants in the bottom sediments off-shore and water systems in river valleys. Analyzed were also the data on migration of the carcinogenic components within Lake Valday (North-western Russia). A method has been proposed for the quantitative estimation of a number of hydro-physical factors through an approximation of experimental data by any equations theoretically proved as well as mathematical solutions of the inverse problems. KEYWORDS Pollutant dispersion; numerical analysis; water bodies; near-to-bottom areas. 1. INTRODUCTION Divides of water bodies, particularly the bottom, are reformers, accumulators and sources of substances and energy. In relation to the consequences of technogeneous impact on water bodies, there often appear the cases when the bottom sediments become a dominant factor of pollution, which affect the phone concentration of pollutants. Until the time, a non-significant attention was paid to the studies of the flux properties on the borders with diverse hydro-physical conditions. It is true about the processes at the "water ­ bottom" divide. However, investigations in the area are greatly upraised at this time, that is caused with certain achievements of modern science, and is related to a need of solving the problem of secondary pollution. The problems of this type appear by accumulation of technogeneous pollutants within bottom sediments. 2. METHODS Investigations are based on a theoretical description of the space-and-time inhomogeneities in migration and accumulation of suspended particles. Main stages of the work are: 1) analysis of the nature data available, 2) development of a hydrodynamic model for interaction between fluxes within the near-to-bottom zone, 3) realization of the model based on numerical algorithms. Besides, the methodological problems are discussed of the pollutant dispersion, with an accent on the bottom sediment pollution areas as well as their accumulation within silt. Evaluations were done of advection and diffusion of technogeneous pollutants. Macro-scale hydro-physical dispersion of pollutants was studied with the use of the following differential equation: 110 16th International Northern Research Basins Symposium and Workshop Petrozavodsk, Russia, 27 Aug. ­ 2 Sept. 2007 (1) c c c c c c c c + u + v + ( w - w ) = ( K x ) + ( K y ) + ( K z ) - + z t x y z x x y y z + Q(t ) ( x - a) ( y - b) ( z - d ), Where is concentration of the pollutant; w its gravitation velocity; is the constant of biochemical destruction; is the "delta"-function; t is the time elapsed; x, y, z are the co-ordinates with basis at the water surface; u, v, w are the components of the flow velocity by the relative co-ordinate axis; x , y , z are the turbulent diffusion coefficients for longitudinal, transversal and vertical directions; Q(t) is the power of the pollutant source at the point (, b, d). In the most of cases, which arise by pollution of shallow water and off-shores, we neglect the vertical transport of pollutant. Used widely is a consideration about the so-called "solid lid" for the cases when the surface water deformations are small in comparison with deep. Considering also are the deep average changes of the hydrodynamic and hydro-chemical parameters without attention to the "buoyancy", i.e. the averaging procedure is simply: c ( x, e, t ) = 1 c( x, y, z , t )dz H 0 H (2) where is the deep of the shallow water body. The vertical transfer in such "bulk" models is described through the boundary conditions on free water surface and bottom. Turbulent fluxes of the pollution particles are as follows: (3) q = - u' c', q = - v ' c', x y where u, v, c - the turbulent fluctuations of the liquid velocity and the concentrations of the pollutant across their average values u, v, ; the hyphen above signifies averaging over the ensemble. Transfer of pollutants across the boundary "water-air" through the molecular film is described by the following equation: qA = M 1d where qA is the mass transfer through the film; is the factor rendering chemical reaction; A the film deep; r the pollutant solubility; 1d is the molecular diffusion coefficient within the surface layer above the water. Investigations of the factors are critically important and will be a focus of the future efforts. The pollution transport to the bottom for the time is as follows: Q = qBT, = n t (5) And the averaged concentration within the bottom silt is (6) c = Q / h , * A ( r A - c), z = 0, (4) where h* is the silt deep. The pollutant flux within silt is described by the following equation: qB * = M 2 d * z ,