Generalized diffusion wave equation with inertial effects

Abstract

A generalized diffusion wave equation, which includes inertial effects, is derived on the basis of the linear analogs of the complete equations of continuity and motion of free‐surface flow. Specializations of this equation lead to four types of diffusion wave models, depending on whether the inertia terms (local and convective) are excluded from or included in the formulation: (1) full inertial, (2) local inertial, (3) convective inertial, and (4) noninertial. Analysis of these diffusion wave models reveals substantial differences in their behavior, particularly with regard to the Froude number dependence of their hydraulic diffusivities. The full inertial and local inertial models have neutral Froude numbers, while the convective and noninertial models do not. In addition, the neutral Froude number of the full inertial model (wide channel with Chezy friction) simulates that of the complete equations (Fr = 2). For low Froude number flows the noninertial model is shown to be a good approximation to the full inertial model. The noninertial model is a better approximation to the full inertial model than either local or convective models.