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Topographically forced long waves on a sheared coastal current. Part 1. The weakly nonlinear response

Clarke, SR; Johnson, ER; (1997) Topographically forced long waves on a sheared coastal current. Part 1. The weakly nonlinear response. J FLUID MECH , 343 131 - 151. 10.1017/S0022112097005685. Green open access

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Abstract

The flow of a constant-vorticity current past coastal topography is investigated in the long-wave weakly nonlinear limit. In contrast to other near-critical weakly nonlinear systems this problem does not exhibit hydraulically controlled solutions. It is shown that near criticality the evolution of the vorticity interface is governed by a forced BDA (Benjamin-Davis-Acrivos) equation. The solutions of this equation are discussed and two distinct near-critical flow regimes are identified. Owing to the non-local nature of the forcing, the first of these regimes is characterized by quasi-steady solutions controlled at the topography with some blocking of the upstream rotational fluid, while in the second regime steady nonlinear wavetrains form downstream of the obstacle with no upstream influence. In the hydraulic limit the velocity band for both of these critical regimes approaches zero.

Type: Article
Title: Topographically forced long waves on a sheared coastal current. Part 1. The weakly nonlinear response
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112097005685
Publisher version: http://dx.doi.org/10.1017/S0022112097005685
Language: English
Additional information: © 1997 Cambridge University Press
Keywords: FLOW, HYDRAULICS, 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/85363
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