The effects of stratification and coastline geometry on the geographical localisation of shelf wave energy.
Doctoral thesis, UCL (University College London).
Variations in shelf geometry mean that a coastal-trapped wave (CTW) mode can propagate within some finite length of shelf but be evanescent outside these regions. These disturbances will be denoted here as localised coastal-trapped waves (ℓCTWs). The subsequent motions produced by such localised variations in shelf geometry, i.e. wave propagation, wave trapping and eddy generation, are discussed in both the coastal-trapped wave (baroclinic) and continental shelf wave (barotropic) limits. Firstly, localised continental shelf waves (ℓCSWs) trapped by local variations in coastline curvature, shelf slope and shelf break distance from the coastal wall are constructed using a WKBJ approximation (accurate for both strong and weak variations) and an expansion about cut-off frequencies (valid for sufficiently weak variations). Comparison with a full numerical study, based on spectral differentiation matrices, of the nonlinear differential eigenvalue problem demonstrates that, in their required limits, both approximations are extremely accurate. The numerical scheme is also extended to discuss how these localised disturbances may be generated by localised wind forcing oscillating at a frequency close to that of the localised modes thereby generating a resonant response in the neighbourhood of the local geometric variation. The second body of work describes efficient and accurate spectral numerical schemes to compute both propagating and evanescent free baroclinic coastal-trapped waves over general depth profiles for arbitrary density profiles in horizontally semi-infinite domains. A novel nonlinear boundary condition is derived that is particularly effective for modes whose offshore decay is weak, as in the long-wave limit. Additionally, geographically localised coastal trapped waves are constructed both asymptotically, using a WKBJ approach, and numerically, using a 3D extension to the highly accurate 2D spectral schemes mentioned above, which allows for the inclusion of arbitrary alongshore variations in offshore depth profile and arbitrary vertical density profiles. Both schemes are then used to demonstrate the importance of stratification, shelf slope and shelfbreak distance from the coastal wall on ℓCTWs. Finally, a new mechanism for vortex generation on continental shelf margins is proposed by considering an incident CTW impinging a geographically localised non-propagating region. The nonlinear governing equations are integrated numerically on a spectral grid with the results used to discuss the interaction of nonlinearity, dispersion and viscosity, and thus the possibility of vortex generation, wave reflection or dissipation, as the incident wave mode approaches the singular region.
|Title:||The effects of stratification and coastline geometry on the geographical localisation of shelf wave energy|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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