Design Model for Thermal Effluents in Rivers

A quasi three-dimensional mathematical model describing the thermal impact of warm water discharges in rivers is presented. The governing equations are obtained integrating along the depth the complete set of the Navier-Stokes equations with Leibniz's rule and assuming that buoyancy forces are negligible. After the analytical integration is performed, in the mass, momentum and energy equations, terms appear that make it possible to account for the effects of the actual geometry of the river's cross section and bottom. The eddy viscosity and thermal diffusivity are taken into account by adopting an algebraic model of turbulence based upon the Prandtl mixing length theory. The numerical model, obtained with a finite difference method, provides the spatial time-dependent distributions of the velocity and temperature fields. The model's results have been satisfactorily checked against field data in the case of thermal discharges into fast moving rivers.