Analysis of thermal impact in tidal rivers and estuaries

The paper presents a far field mathematical model for numerical simulation of transient one or two-dimensional thermal distributions in regions with severe reversing flow conditions. The Eulerian formulation employs the integral form of the conservation principles for mass and thermal energy. The two-dimensional (2 D) solution area is spanned by discrete elements of variable size and shape. The three-dimensional geometry of the flow region is accounted for by spatially intergrating over the enclosure surfaces of the discrete element. The derivation of the two-dimensional depth-averaged temperatur equations includes the constributions of the vertical variations of velocity and temperature. Surface heat transfer as well as turbulent effects are taken into account. Important mathematical and computational features of the model are summarized. There is a discussion of the four main algorithms, necessary to treat flow regions with complex shoreline geometries, viz. (i) specification of the boundary (ii) determination of all discrete element midpoints lying within the (possibly multiconnected) solution area (iii) construction of discrete elements of irregular geometry exactly matching the (curved) boundary, (iv) treatment of boundary condiditons and numerical solution of the resulting mathematical system of weakly coupled, ordinary differential equations derived from the conservation principles. Preliminary results of a computer simulation are compared with the available data for a section of the Lower Elbe river. The calculation of the two-dimensional temperature distribution includes existing power plants and industrial sites. (orig.)