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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 Forbes
The 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 Mechanics

Volume

461

Pagination

387-407

ISSN

0022-1120

Department/School

School of Natural Sciences

Publisher

Cambridge University Press

Place of publication

New York

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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