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Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity
journal contribution
posted on 2023-05-16, 13:31 authored by McCue, S, Lawrence ForbesLawrence ForbesThe free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.
History
Publication title
Journal of Fluid MechanicsVolume
461Pagination
387-407ISSN
0022-1120Department/School
School of Natural SciencesPublisher
Cambridge University PressPlace of publication
New YorkRepository Status
- Restricted