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- Title
NEW SHALLOW FLOWS OVER AN OBSTACLE.
- Authors
BROAD, A. S.; PORTER, D.; SEWELL, M. J.
- Abstract
Lowest-order shallow water theory is applied to flow, in a single vertical plane, over a wide class of monotonic mountains. Many new flows are described. These include steady continuous smoothly bifurcating flows, in which the fluid speed and the free surface profile bifurcate smoothly at the apex of the mountain, unless the mountain is locally parabolic there. In the latter case the free surface bifurcation is known to be abrupt and not smooth at the apex, but we show that this is the exception. We demonstrate that the fluid speed and free surface shape are sensitive to the mountain shape near the apex. Pseudo-steady flows, containing a bore travelling upstream away from the obstacle, are exhibited. In some cases the bore relieves what would otherwise be a blocked continuous flow. If the incoming Froude number is not too large, the bore can lift the fluid so that it subsequently flows over the obstacle either freely or, if energy dissipation is minimized at the bore, with a bifurcation at the apex. Such bores can also coexist with what would otherwise be a bifurcating or a free continuous flow. The strength ranges which are admissible for all these bores are determined. A complete geometrical representation of all the possible bores is given, in a three-dimensional parameter space for the first time.
- Subjects
WATER depth; HYDRAULICS; SPEED; FREE surfaces; FLUID mechanics; BIFURCATION theory; ENERGY dissipation; BORES (Tidal phenomena)
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 1997, Vol 50, Issue 4, p625
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/50.4.625