Flood Routing in an Irregular Channel

The movement of flood waves in rivers is governed by the equations of continuity and momentum. Because these are partial differential equations of the hyperbolic class, they may be converted into a set of four simultaneous ordinary differential equations. This transformation and the subsequent solution of the ordinary equations is known as the method of characteristics. The writers applied Massau’s method to subcritical flow in an irregular channel without simplifying its geometry. The results of the mathematical model agree with the way prototype floods are known to behave. The crests of large floods traveled faster and subsided less rapidly than the crests of small floods. An increase in roughness decreased the wave velocity and increased the attenuation. The span of loop rating curves increased with the rate of rise and fall of the stage, and hydrographs at successive stations downstream satisfied the equation of continuity. The method of characteristics avoids certain sources of error that sometimes arise when finite difference methods are applied directly to hyperbolic equations. The writers found the solutions to be stable and well-behaved. Moreover, the characteristic approach may be interpreted in a way that provides a good deal of physical insight to the problem of wave movements.