The Influence Of Mixed Derivatives On TheMathematical Simulation Of Pollutants Transfer

Both turbulent diffusion and dissolved matter dispersion are anisotropic processes. From the formal point of view this fact is expressed by the tensor form of the transfer coefficients. As a result, mixed derivatives of concentration appear in the transport equations. However many authors, for the sake of simplicity, neglect these derivatives. The paper deals with investigation of the influence of cross-derivatives, exerted on the results of calculations. Theoretical and numerical analyses lead to the conclusion, that investigated terms are of great importance and should not be neglected. 1 Governing equations Two main versions of the dissolved matter conservation law are commonly used for description of the mass transfer processes. The first one describes the timeaveraged turbulent transfer, and can be written as follows (see e.g. TASK Committee [1]): dc — + (uV)c = DAc-divniT + ]r^ (1) fy i where: c , u time-averaged concentration and velocity, D molecular diffusivity, $ source functions (i = l....Is), m? turbulent unit mass flux, defined as the time-averaged product of concentration c' and velocity fluctuations u m^-nV (2) The second relation is the depth-averaged version of the Eq.l (see e.g. Rutherford [2]) : Transactions on Ecology and the Environment vol 14, © 1997 WIT Press, www.witpress.com, ISSN 1743-3541