Revisiting overland runoff modeling: Mixed flows and pseudo-kinematic waves

Abstract

Overland flow resulting from the rainfall-runoff transformation is an important hydrological process in agricultural and urban watersheds, occurring in the form of a thin fluid sheet moving on rough and relatively steep terrain. Mixed flows involving moving critical points are frequent, especially in urban drainage, but a method to deal with these flows is so far not available. In this work a new and robust solution method for the computation of equilibrium mixed flows is presented, resulting in solutions not available so far. Based on these results, the convergence features to mixed flows of a dynamic wave model developed are investigated choosing suitable tailwater boundary conditions. The new solution method developed for mixed flows reveals that pseudo-uniform flow profiles are closer to dynamic wave profiles than kinematic profiles. It allowed the definition of a new kinematic-wave truncation of the momentum equation, the pseudo-kinematic wave, suitable for unsteady rainfall-runoff modeling. The new shallow water wave approach proposed is closer to dynamic waves than the standard kinematic approach and permits to simulate unsteady overland flows more accurately over a wider range of conditions, e.g. for kF₀² > 5 and F₀ < 2. The dynamic wave model presented is compared with experiments, other computational solutions, and two new analytical solutions developed, one for steady flows and another for unsteady flows. The steady mixed flow profiles are compared with experiments and results of the dynamic wave model, detailing the formation of critical points. Dynamic, kinematic and pseudo-kinematic waves are extensively compared for flow conditions where the kinematic wave is invalid. Finally, the roll wave development, which is not detailed so far in overland flow under rainfall, is considered to settle an upper validity limit of the new pseudo-kinematic wave approach.