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The Initial Phase of the Rising Hydrograph of Turbulent Free Surface Flow with Unsteady Lateral Inflow
Author(s) -
Brutsaert Wilfried
Publication year - 1968
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/wr004i006p01189
Subject(s) - inflow , kinematic wave , turbulence , flow (mathematics) , open channel flow , geometry , plane (geometry) , mechanics , hydraulics , mathematics , hydrograph , geology , surface runoff , physics , thermodynamics , ecology , biology
An exact solution is obtained for the de Saint Venant equations describing flow over a plane or in a very wide channel with a general turbulent friction law and with a uniform lateral inflow as a power function of time valid for the space‐time domain bounded by 0 ≤ x ≤ L , t = 0, by the forward characteristic originating at x = 0, t = 0, and by the backward characteristic originating at x = L , t = 0. The quantity L denotes the length of the flow region, x the direction of flow, and t the time. We found that, for very small values of time, the uniform flow velocity is everywhere directly proportional to t regardless of the nature of the lateral inflow. For a very large slope or a large roughness of the plane, or for a very small constant lateral inflow, the present solution reduces to the result obtainable with the kinematic wave approximation. (Key words: Hydraulics; overland flows; runoff)