Modeling Rapidly Varied Flow in Tailwaters

Abstract

An understanding of the downstream propagation of sharp‐fronted, large‐amplitude waves of relatively short period is important for describing rapidly varying flows in tailwaters of hydroelectric plants and following the breach of a dam. We developed a numerical model of these waves by first identifying the primary physical processes and then performing an analysis of the solution. A linear analysis of the dynamic open channel flow equations provides relationships describing flow wave advection, diffusion, and dispersion in rivers. A one‐dimensional diffusion wave model modified for application to tailwaters simulates the important physical processes and is straightforward to apply. The “modified equation” and von Neumann analyses provide insight into the effects of numerical parameters θ, Δ x , and Δ t upon stability and dissipative and dispersive behavior of the solution, but the Hirt analysis is found to yield incorrect phase relationships. The capability and accuracy of the model are enhanced when physical diffusion of a river wave is balanced by numerical diffusion in the model. Field studies were conducted in two greatly different tailwaters to assess our understanding of large‐scale, rapidly varying flow waves. The accurate simulation of waves having wide‐ranging amplitudes, shapes, periods, and base flows attests to the soundness of both the physical basis of the model and the numerical solution technique. These studies reveal that diffusion of short‐period waves in natural, free‐flowing rivers is significant and that inertia is negligible.