Trapped modes in coastal waveguides

Johnson, E. R.; Rodney, J.T.; Kaoullas, George

doi:10.1016/j.wavemoti.2011.08.004

Cited by 4 publications

(8 citation statements)

References 9 publications

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“…In the similar acoustic waveguide problem Biggs (2012) follows Gridin et al (2005), using symmetry and Laguerre interpolation to treat the semi-infinite alongwaveguide direction directly. Both treatments are accurate and efficient although for the present problem the discretisation in Johnson et al (2012) seems to require smaller matrices.…”

Section: The Numerical Methodsmentioning

confidence: 94%

“…The small parameter , which for the underlying curved shelf gives the non-dimensional alongshelf length scale −1 for both the curvature changes and the cross-shelf profile changes, must be taken to determine only the magnitude of the alongshore variations in bend angle, with = 0 giving a straight coast. Follow Postnova & Craster (2008) and Johnson et al (2012) by initially taking the scale for γ to be and introducing the expansions…”

Section: An Underlying Straight Shelfmentioning

confidence: 99%

“…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%

“…Accurate explicit CSWs solutions are found for relatively short along-shore variations. The asymptotic results of Postnova & Craster (2008) and Johnson et al (2012) are generalised to arbitrary offshore depth profiles with alongshore variations in coastline curvature as well as incorporating the full open-ocean boundary condition. Accurate numerical solutions demonstrate that the expansion based on fractional curvature change is more accurate in a number of cases than the expansion about straight coasts, even when the curvature is small.…”

Section: Introductionmentioning

confidence: 99%

“…As verification for the asymptotic schemes modes are calculated numerically in §4 using highly efficient spectral approximations. The numerical methods allow for arbitrary offshore depth boundary conditions and depth profiles, including profiles that are discontinuous at the shelf ocean boundary, such as the classical exponential depth profile of Buchwald & Adams (1968), and offer an extension to the numerical methods presented in Postnova & Craster (2008) and Johnson et al (2012). The numerical and asymptotic solutions are then used to discuss the effects of coastline curvature and alongshore variations in offshore depth profile on CSWs in §5.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Numerical Methodsmentioning

confidence: 94%

Section: An Underlying Straight Shelfmentioning

confidence: 99%