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Topographically forced long waves on a sheared coastal current. Part 2. Finite amplitude waves

Clarke, SR; Johnson, ER; (1997) Topographically forced long waves on a sheared coastal current. Part 2. Finite amplitude waves. J FLUID MECH , 343 153 - 168. 10.1017/S0022112097005697. Green open access

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Abstract

This paper analyses the finite-amplitude flow of a constant-vorticity current past coastal topography in the long-wave limit. A forced finite-amplitude long-wave equation is derived to describe the evolution of the vorticity interface. An analysis of this equation shows that three distinct near-critical regimes occur. In the first the upstream flow is restricted, with overturning of the vorticity interface for sufficiently large topography. In the second quasi-steady nonlinear waves form downstream of the topography with weak upstream influence. In the third regime the upstream rotational fluid is partially blocked. Blocking and overturning are enhanced at headlands with steep rear faces and decreased at headlands with steep forward faces. For certain parameter values both overturning and partially blocked solutions are possible and the long-time evolution is critically dependent on the initial conditions. The reduction of the problem to a one-dimensional nonlinear wave equation allows solutions to be followed to much longer times and parameter space to be explored more finely than in the related pioneering contour-dynamical integrations of Stern (1991).

Type: Article
Title: Topographically forced long waves on a sheared coastal current. Part 2. Finite amplitude waves
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112097005697
Publisher version: http://dx.doi.org/10.1017/S0022112097005697
Language: English
Additional information: © 1997 Cambridge University Press
Keywords: HYDRAULICS, FLOWS, SHELF
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/85367
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