Flood routing in mild-sloped rivers—wave characteristics and downstream backwater effect

Unsteady flow routing in a mild-sloped river with gradually varying flow depth induced by the downstream backwater effect is theoretically investigated. The Saint-Venant equations and other routing models are linearized at the base flow state, a steady and spatially varying subcritical flow represented by the M1 or M2 water surface profile. The linear stability analysis is adopted to study the physical mechanisms responsible for wave attenuation or amplification, and wave retardation or acceleration in open channels when the flow is spatially varying. Analytical descriptions of the propagation characteristics such as wave celerity and wave attenuation factor for all range of wave numbers are derived and expressed in terms of channel property, steady uniform flow Froude number, dimensionless wave number, base flow depth and base flow pressure gradient. The downstream backwater effect on wave characteristics of various widely used flood routing models is discussed.