Abstract
Error equations for kinematic wave and diffusion wave approximations were derived for time-independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF ≥ 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF ≥ 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K.
Original language | English |
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Pages (from-to) | 1771-1790 |
Number of pages | 20 |
Journal | Hydrological Processes |
Volume | 19 |
Issue number | 9 |
DOIs | |
Publication status | Published - Jun 15 2005 |
Keywords
- Critical flow depth
- Diffusion wave
- Dynamic wave
- Kinematic wave
- St. Venant equations
- Steady flow
- Upstream boundary
- Zero depth gradient
ASJC Scopus subject areas
- Water Science and Technology