Author(s): Paul Samuels; Mark Morris
Linked Author(s): Paul Samuels
Keywords: No Keywords
Abstract: Most models of the flow over an embankment or through a breach treat the flow as that over a broad-crested weir. This may be appropriate when the flow width is large compared with the depth, and the streamlines of the flow in the reservoir towards the embankment or breach nearly normal to the crest. However, evidence from laboratory and large scale field tests (such as in the EC IMPACT project) show strong curvature of the flow towards a narrow breach with approximately semi-elliptical or semi-circular shaped water profiles in plan for the reservoir upstream of the breach. This paper presents a new analytic model for the two dimensional flow towards a slot in an otherwise solid flow boundary. The surface profiles predicted from the model are semi-elliptical in plan, becoming semi-circular in the limit of an infinitesimally thin slot. Analysis of this latter idealized case shows that critical flow occurs at a radial distance inside the reservoir of rc given by: r_c~2=27Q~2/8gπ~2E~3 where Q is the discharge through the breach and E is the total energy level in the reservoir measured above the base of the breach. Non-dimensionalising the horizontal distance along the streamlines leads to a new universal solution for the water level profile for this idealised case. This solution provides insight into both the erosion mechanisms that control breach growth and the validity of assuming flow is similar to a broad-crested weir.
Year: 2010