Abstract
Chapter 6 deals with the lowest order shallow-water approximation in one space dimension, representing what is commonly known as open-channel flow theory. The equations of de Saint-Venant are derived for channels of arbitrary cross-sectional shape. Non-prismatic channels, lateral flow, and the effect of flood plain integration in the cross section are discussed. Conservation forms and alternative formulations of the governing equations are also presented. Further truncation of the equations is pursued, and the simplest possible models of free-surface flow are established. Extensions of the equations to nonlinear dispersive waves and wave-current interaction are also presented. The concept of radiation stresses is introduced and the shallow-water equation models are modified to account for short waves.
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