Analysis of River Wave Types

Abstract

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.

Simple wave and monoclinal wave models: River flow surge applications and implications

“…[22] Ferrick [1985] developed a dimensionless system equation for the Saint Venant equations where the changes in dominant terms are reflected in the relative magnitudes of several scaling parameters. One parameter, a dimensionless time F I , scales the slope and flow resistance contributions relative to that of inertia…”

“…[3] The simple wave is a type of gravity wave, characterized by dominant inertia and negligible effects of bed slope and flow resistance [Ferrick, 1985]. In free-flowing rivers the bed slope and flow resistance effects increase with travel time and distance, and eventually become large.…”

Applicability criteria of the variable parameter Muskingum stage and discharge routing methods

“…These simplified hydraulic methods also involve a varied degree of complexity in computation. Flood routing studies based upon simplified methods, derived either directly or indirectly from the Saint-Venant equations, are perceived as inherently less accurate than those based upon the numerical solution of the full SaintVenant equations [Ferrick, 1985]. However, the simplified models continue to be of valuable tool for river engineers who want rapid access to a broad view of flood behavior in their rivers for planning and operation purposes, especially when sparse information on cross-sectional details are available.…”

“…However, the simplified models continue to be of valuable tool for river engineers who want rapid access to a broad view of flood behavior in their rivers for planning and operation purposes, especially when sparse information on cross-sectional details are available. Further, numerical problems arise while solving the full Saint-Venant equations for studying flood wave movement when the magnitudes of different terms of the momentum equation are widely varying [Ferrick, 1985]. By analyzing different wave types, Ferrick [1985] suggested the use of appropriate wave type equations for obtaining accurate solutions without facing numerical problems, and argued that the use of more complete equations may not yield more accurate river wave simulations for all wave types.…”

“…Further, numerical problems arise while solving the full Saint-Venant equations for studying flood wave movement when the magnitudes of different terms of the momentum equation are widely varying [Ferrick, 1985]. By analyzing different wave types, Ferrick [1985] suggested the use of appropriate wave type equations for obtaining accurate solutions without facing numerical problems, and argued that the use of more complete equations may not yield more accurate river wave simulations for all wave types. This argument is now substantiated by the wide spread use of the simplified routing methods like the variable parameter Muskingum-Cunge (VPMC) method [Ponce and Yevjevich, 1978] and its variants [Ponce and Chaganti, 1994;Ponce and Lugo, 2001] in practice [Fread, 1990; U.S. Army Corps of Engineers, 2002].…”