Geographically localised shelf waves on curved coasts

Kaoullas, George; Johnson, E. R.

doi:10.1016/j.csr.2010.08.002

Cited by 7 publications

(15 citation statements)

References 20 publications

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“…the curvature goes to zero at infinity) a weaker condition than the one in JLP, where the curvature has compact support. Also, in Kaoullas and Johnson (2010b) trapped modes are constructed without restricting attention to weak curvature and thus the behaviour of the solutions is examined when the curvature exceeds the upper bound of JLP. These three methods rely heavily on the Neumann boundary condition approximation, at the shelf-ocean boundary, which is valid only in the long wave limit.…”

Section: Introductionmentioning

confidence: 99%

Isobath variation and trapping of continental shelf waves

Kaoullas

Johnson

2012

J. Fluid Mech.

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Since Trösch (Proceedings of the 4th International Conference on Applied Numerical Modeling, Tainan, Taiwan, 1984 (ed. H. M. Hsia, Y. L. Chou, S. Y. Wang & S. J. Hsieh) Science and Technology Series, vol. 63, 1986, pp. 307–311. American Astronautical Society) found trapped sub-inertial oscillations in computations of low-frequency variability in the Lake of Lugano, models of trapping have generally considered evenly spaced isobaths parallel to shorelines with approximate boundary conditions at any shelf–ocean boundary. Here an asymptotic analysis for slowly varying topography and accurate spectral computations demonstrate trapping on non-rectilinear shelves. It is shown that changes in any of three factors, isobath curvature, distance from the coast and the shelf-break, and the slope at the shelf-break, are sufficient on their own to give trapping. Continental shelves that abut smoothly onto the open ocean are considered thus avoiding the shelf–ocean boundary condition approximation and allowing the accuracy of previous approximations to be assessed.

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Section: Introductionmentioning

confidence: 99%

Isobath variation and trapping of continental shelf waves

Kaoullas

Johnson

2012

J. Fluid Mech.

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“…Existence proofs, asymptotic expansions and numerical computations for CSWs are given in Johnson et al (2006), Postnova & Craster (2008), Kaoullas & Johnson (2010) and Johnson et al (2012). All these studies use an approximate Neumann boundary condition at the shelf-ocean boundary.…”

Section: Introductionmentioning

confidence: 99%

Localised continental shelf waves: geometric effects and resonant forcing

Rodney

Johnson

2015

J. Fluid Mech.

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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 ( CTWs) here, exist only at certain discrete frequencies lying below the maximum frequency for propagating shelf waves. The purpose of this paper is to obtain these frequencies and construct, both analytically and numerically, and discuss CTWs 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 a alongshore perturbation in offshore depth profile varies slowly over the same length scale then CTWs can be constructed using WKBJ theory. Two subcases are described: (i) if the propagating region is sufficiently long that the offshore structure of the CTW 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 CTW 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 CTWs shows that both theories are extremely accurate with the WKBJ theory having a significantly wider range of applicability and remaining accurate even when the underlying shelf curvature is small. An idealised model for the generation of CTWs 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 CTW then the wind stress excites energetic motions in the region of maximum curvature, creating a significant localised response far from the forcing region.

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“…For example, Mysak et al [1979] applied linear wave theory applied to double-exponential approximations of coastal depth profiles in the Pacific ocean, whilst Gill and Schumann [1979] attempted to predict the path of Agulhas using an idealized representation of continental slope and deep ocean in a two-layer model. Linear shelf wave theory has since been extended to describe more realistic configurations such as continental shelves with alongshore depth variations [Johnson, 1985;Johnson and Davey, 1990], curved coastlines [Kaoullas and Johnson, 2010;Johnson et al, 2012], and arbitrary isobath variations Kaoullas and Johnson, 2012].…”

Section: Shelf Waves and Coastal Currents In The Laboratorymentioning

confidence: 99%