eprintid: 1474258
rev_number: 30
eprint_status: archive
userid: 608
dir: disk0/01/47/42/58
datestamp: 2016-01-28 16:17:57
lastmod: 2020-02-13 00:15:31
status_changed: 2016-01-29 15:06:51
type: article
metadata_visibility: show
creators_name: Rodney, JT
creators_name: Johnson, ER
title: Localised continental shelf waves: geometric effects and resonant forcing
ispublished: pub
divisions: UCL
divisions: A01
divisions: B04
divisions: C06
divisions: F59
keywords: shallow water flows, topographic effects, waves in rotating fluids
note: © 2015 Cambridge University Press
abstract: Alongshore variations in coastline curvature or offshore depth profile can create localised regions of shelf-wave propagation with modes decaying outside these regions.
These modes, termed localised continental shelf waves (`CSWs) here, exist only at certain discrete frequencies lying below the local maximum frequency, and above
the far-field maximum frequency, for propagating shelf waves. The purpose of this paper is to obtain these frequencies and construct, both analytically and numerically, and discuss `CSWs for shelves with arbitrary alongshore variations in offshore depth profile and coastline curvature. If the shelf curvature changes by a small fraction of its value over the shelf section of interest or an alongshore perturbation in offshore depth
profile varies slowly over the same length scale then `CSWs can be constructed using WKBJ theory. Two subcases are described: (i) if the propagating region is sufficiently long that the offshore structure of the `CSW varies appreciably alongshore then the frequency and alongshore structure are found from a sequence of local problems; (ii) if the propagating region is sufficiently short that the alongshore change in offshore structure of the `CSW is small then the alongshore modal structure is given in an explicit, uniformly valid form. A separate asymptotic theory is required for curvature perturbations to shelves that are otherwise straight rather than curved. Comparison with highly accurately numerically determined `CSWs shows that both theories are extremely accurate, with the WKBJ theory having a significantly wider range of applicability. An idealised model for the generation of `CSWs is also suggested. A localised time-periodic wind stress generates an evanescent continental shelf wave in the far field of a localised mode where the coast is almost straight and the response on the shelf is obtained numerically. If the forcing frequency is close to that of an `CSW then the wind stress excites energetic motions in the region of maximum curvature, creating a significant localised response possibly far from the forcing region.
date: 2015-12
date_type: published
official_url: http://dx.doi.org/10.1017/jfm.2015.588
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1058540
doi: 10.1017/jfm.2015.588
lyricists_name: Johnson, Edward
lyricists_id: ERJOH80
actors_name: Johnson, Edward
actors_id: ERJOH80
actors_role: owner
full_text_status: public
publication: Journal of Fluid Mechanics
volume: 785
pagerange: 54-77
issn: 0022-1120
citation:        Rodney, JT;    Johnson, ER;      (2015)    Localised continental shelf waves: geometric effects and resonant forcing.                   Journal of Fluid Mechanics , 785    pp. 54-77.    10.1017/jfm.2015.588 <https://doi.org/10.1017/jfm.2015.588>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1474258/7/Rodney_Johnson_local_CSW_JFM_v31a.pdf