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FREE-SURFACE ADJUSTMENT AND TOPOGRAPHIC WAVES IN COASTAL CURRENTS

JOHNSON, ER; DAVEY, MK; (1990) FREE-SURFACE ADJUSTMENT AND TOPOGRAPHIC WAVES IN COASTAL CURRENTS. J FLUID MECH , 219 273 - 289. 10.1017/S0022112090002944. Green open access

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Abstract

The adjustment of rotating free-surface flow over a step-like escarpment abutting a vertical wall is discussed in the context of the shallow-water equations. The problem is simplified by considering an escarpment of small fractional depth, so that on the slow topographic timescale the initial, fast Poincaré and Kelvin wave adjustment of the free surface is effectively instantaneous, and further simplified by considering the surface displacement to be small compared with the escarpment height so that particle velocities are negligible during the topographic adjustment. Direct solution of the resulting linear system is not straightforward as arbitrarily small-scale motions are generated at sufficiently large times. The problem is reduced by a Green's function technique to one spatial dimension and the wall boundary layers resolved by introducing a scaling based on previously obtained limit solutions. Solutions verify the information-propagation arguments of Johnson (1985) and Gill et al. (1986) and also show interchange of fluid across the escarpment as eddies formed as the current crosses the step travel along the step with shallow water to their right. The pattern of evolution of the system is independent of the direction of the flow, depending solely on the sign of the topographic step. If the escarpment is such that topographic waves travel away from the wall, then a tongue of fluid moves outward along the step: the initial jet along the wall is diverted to flow parallel to, rather than across, the step. If waves travel towards the wall then the current is pinched into the wall and fluid crosses the escarpment in a thinning jet.

Type: Article
Title: FREE-SURFACE ADJUSTMENT AND TOPOGRAPHIC WAVES IN COASTAL CURRENTS
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112090002944
Publisher version: http://dx.doi.org/10.1017/S0022112090002944
Language: English
Additional information: © 1990 Cambridge University Press
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/1325361
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