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