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Asymptotic expansion for steady state overland flow
Author(s) -
Parlance J.Y.,
Hogarth W.,
Sander G.,
Rose C.,
Haverkamp R.,
Surin A.,
Brutsaert W.
Publication year - 1990
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr026i004p00579
Subject(s) - kinematic wave , kinematics , flow (mathematics) , mathematics , plane (geometry) , diffusion , steady state (chemistry) , shallow water equations , mathematical analysis , geometry , mechanics , classical mechanics , physics , surface runoff , ecology , chemistry , biology , thermodynamics
The full Saint Venant equations of overland flow on a plane are often replaced by simpler models. The errors in the kinematic and the diffusion models are estimated by comparing their predictions with the exact numerical solution of the Saint Venant equations under steady state conditions. It is shown that the two approximate models can have significant errors even for critical flow and fairly large kinematic wave numbers. When the kinematic approximation is inaccurate, the improvement of the diffusion approximation seems modest. For the same level of mathematical complexity as the diffusion approximation, a far more accurate approximation is proposed when the kinematic wave number is large. It is then possible to split the solution of the Saint Venant equation in two regions, one near the downstream end of the plane and the other covering most of the plane.