Analysis of River Wave Types

In this paper we consider long-period, shallow-water waves in rivers that are a consequence of unsteady flow. River waves result from hydroelectric power generation or flow control at a dam, the breach of a dam, the formation or release of an ice jam, and rainfall-runoff processes. The Saint-Venant equations are generally used to describe river waves. Dynamic, gravity, diffusion, and kinematic river waves have been defined, each corresponding to different forms of the momentum equation and each applying to some subset of the overall range of river hydraulic properties and time scales of wave motion. However, the parameter ranges corresponding to each wave description are not well defined, and the transitions between wave types have not been explored. This paper is an investigation into these areas, which are fundamental to river wave modeling. The analysis is based on the concept that river wave behavior is determined by the balance between friction and inertia. The Saint-Venant equations are combined to form a system equation that is written in dimensionless form. The dominant terms of the system equation change with the relative magnitudes of a group of dimensionless scaling parameters that quantify the friction-inertia balance. These scaling parameters are continuous, indicating that the various river wave types and the transitions between them form a spectrum. Additional data describing the physical variability of a river and wave are incorporated into the analysis by interpreting the scaling parameters as random variables. This probabilistic interpretation provides an improved estimate of the friction-inertia balance, further insight into the continuous nature of wave transitions, and a measure of the reliability of wave type assessments near a transition. Case studies are used to define the scaling parameter ranges representing each wave type and transition and to provide data with which to evaluate the usefulness of the analysis for general application.