Victor Miguel Ponce

Effect of Cross-Sectional Shape on Free-Surface Instability

The effect of cross sectional shape on free-surface hydrodynamic instability has been analyzed. The characterizing parameter is the dimensionless relative kinematic wave celerity c drk = β - 1, in which p is the exponent of the normal discharge-flow area rating. Two generic types of cross-sectional shapes are identified: (1) those of constant c drk , and (2) those of variable c drk . Three cross-sectional shapes of constant c drk are: (1) hydraulically wide, with c drkM = 2/3, (2) triangular, with c drkM = 1/3, and (3) inherently stable, with c drk = 0 (Manning or Chezy). (The subscript M refers to Manning friction). Cross-sectional shapes of variable c drk include trapezoidal, rectangular, and circular shapes. Two asymptotic cross-sectional shapes are identified: (1) hydraulically wide, and (2) hydraulically narrow. These theoretical cross-sections set limits to the range of variation of c drk for trapezoidal and rectangular shapes. The hydraulically wide channel sets the upper limit, with c drkM → 2/3; the hydraulically narrow channel sets the lower limit, with c drk → 0. Two types of stable channels are identified: (1) inherently stable, and (2) stable. An inherently stable cross section is such that the Vedernikov number V is identically zero for all Froude numbers. A stable cross section is such that V ≤ 1 for Froude numbers in the range F ≤ F ns , in which F ns is a design neutral-stability Froude number. A stable cross-sectional shape is designed by setting c drk and the related cross-sectional parameter δ to match a certain choice of F ns . The resulting stable cross-sectional shape is much narrower that the comparable inherently stable shape.

Effect of Vedernikov Number on Overland Flow Dynamics

The effect of the dynamic hydraulic diffusivity in kinematic-with-diffusion overland flow modeling has been tested. Unlike the kinematic hydraulic diffusivity, the dynamic hydraulic diffusivity is a function of the Vedemikov number. The results of numerical experiments showed a small lag in the rising limb when comparing two equilibrium rising hydrographs using kinematic and dynamic hydraulic diffusivities. The existence of the lag is attributed to the error of the solution that specifically excludes inertia. The error was quantified by integrating the absolute value of the difference between the two rising hydrographs, dividing this difference by the total runoff volume and expressing it as a percentage. The error is small and likely to be within 0.35 percent for a wide range of realistic flow conditions. Since the dynamic effect is shown to be small throughout a wide range of bottom slopes, a diffusion wave model with inertia may be all that is required to model the overland flow dynamics.