Analysis of Linear and Monoclinal River Wave Solutions

Abstract

Linear dynamic wave and diffusion wave analytical solutions are obtained for a small, abrupt flow increase from an initial to a higher steady flow. Equations for the celerities of points along the wave profiles are developed from the solutions and are related to the kinematic wave and dynamic wave celerities. The linear solutions are compared systematically in a series of case studies to evaluate the differences caused by inertia. These comparisons use the celerities of selected profile points, the paths of these points on the x-t plane, and complete profiles at selected times, and indicate general agreement between the solutions. Initial diffusion wave inaccuracies persist over relatively short time and distance scales that increase with the wave diffusion coefficient and Froude number. The nonlinear monoclinal wave solution parallels that of the linear dynamic wave, but is applicable to arbitrarily large flow increases. As wave amplitude increases, the monoclinal rating curve diverges from that for a linear wave, and the maximum Froude number and energy gradient along the profile increase and move toward the leading edge. A monoclinal-diffusion solution for the diffusion wave equations is developed and dynamic wave-diffusion wave comparisons are made over a range of amplitudes with the same case studies used for linear waves. General dimensionless monoclinal-diffusion profiles exist for each depth ratio across the wave, whereas corresponding monoclinal wave profiles exhibit minor, case-specific Froude number dependence. Inertial effects on the monoclinal profiles occur near the leading edge, increase with the wave amplitude and Froude number, and are responsible for the differences between the dimensionless profiles.