Diffusion of floodwaves

Floodwaves may be approximated as an advection-diffusion process when the typical Froude number is much smaller than one. The study refers to the effect of cross-sectional shape on the propagation of a single-peaked flood in a simple river having constant width, slope and roughness. The results are interesting in terms of how exact a shape geometry should be evaluated before proceeding to a detailed numerical computation of river floodwaves. The problem is generally solved by introducing a number of simplifying assumptions that do not detract from the essence of floodwave diffusion. The main parameters retained are the diffusion coefficient and the shape factor. The formulation of the problem is closed with appropriate boundary and initial conditions. The results of the numerical study are discussed in detail and expressions are presented for the main features of the floodwave, including the arrival of the wave front and the wave peak, as well as the peak discharge in terms of diffusion and cross-sectional shape. Using a different set of parameters, it can be demonstrated that the last two effects may be dropped for preliminary computations. Accordingly, the prediction of floodwave propagation can easily be accomplished.