@article{discovery1474258,
           month = {December},
           title = {Localised continental shelf waves: geometric effects and resonant forcing},
          volume = {785},
            note = {{\copyright} 2015 Cambridge University Press},
           pages = {54--77},
            year = {2015},
         journal = {Journal of Fluid Mechanics},
            issn = {0022-1120},
             url = {http://dx.doi.org/10.1017/jfm.2015.588},
        keywords = {shallow water flows, topographic effects, waves in rotating fluids},
        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.},
          author = {Rodney, JT and Johnson, ER}
}