Abstract
Singular perturbation techniques are used to obtain an approximate solution of the flood routing problem. The first-order outer solution is given by the kinematic-wave approximation. Singularities in this outer solution then lead to two inner solutions: one that follows a kinematic shock as it moves downstream and one either at the downstream boundary in subcritical flow or at the upstream boundary in supercritical flow. Solutions calculated in each of these subregions allow conclusions to be drawn about the relative importance of various terms in the momentum equation. The inner and outer solutions are combined to obtain composite solutions for flow depths and flow rates, and a numerical example is worked.
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