Applicability of Kinematic, Noninertia, and Quasi-Steady Dynamic Wave Models to Unsteady Flow Routing

Abstract

Propagation of flood waves in an open channel can be mathematically approximated by the Saint-Venant equations (dynamic wave) or by their simplifications including the kinematic wave, noninertia wave, gravity wave, and quasi-steady dynamic wave models. All of these wave approximations differ not only in the physical propagation mechanism, but also in the degree of complexity involved in computation. In order to efficiently implement the approximate wave models for flood routing, their criteria of applicability should be developed. The applicability of the kinematic wave, noninertia wave, and quasi-steady dynamic wave approximations to the full dynamic wave equations for unsteady flow routing is examined by comparing the propagation characteristics of a sinusoidal perturbation to the steady gradually varying flow for different simplified wave models. Development of the applicability criteria provides a guideline for selecting an appropriate wave model for unsteady flow modeling, thus enabling an assessment of the capabilities and limitations of different simplified wave models. By using the linear stability analysis, the derived criteria can be expressed in terms of dimensionless physical parameters that represent the unsteadiness of the wave disturbance, characteristics of the downstream boundary condition (backwater effect), and the location along the channel. The developed criteria are for a specific point and time, thereby providing a more refined indication than the integrated criteria based on the testing for a hydrograph found commonly in the literature. In this study, we have justified whether the simplified wave models such as the kinematic, noninertia, or gravity wave models would be appropriate and reliable approximations to the full Saint-Venant equations with a comparable accuracy for a given flow condition. The downstream backwater effect has been taken into consideration in the developed criteria for broader engineering applications. One hypothetical example is presented for illustration.