The asymptotic wave form for a space-limited perturbation in open channels

Abstract

Through a spectral analysis of the linearized Saint Venant equations, it is shown that any space-limited perturbation of an otherwise steady flow evolves into a gaussian form which attenuates smoothly with time, being the result of the contribution of the longest forward spectral components. It is also shown that the shortest forward and backward spectral component contributions, relevant for intermediate times, preserve the initial wave form but attenuate exponentially. Nonlinear effects are briefly discussed. It is postulated that, due to the filtering behaviour of open channels, it is expected that, in addition to a gaussian wave form, only steps and sinusoids should be observed asymptotically.