Project Summary

Much of the energy measured near coastlines is contained in low frequency waves with periods of a few days, known as continental shelf waves (CSWs), existing due to the interaction of depth changes and the Earth's rotation. CSWs decaying both away from the coast and along the shelf are called trapped CSWs (tCSWs) which show higher than normal energy in the low-frequency horizontal velocity field, thus affecting the stirring, nutrient and pollution concentrations at certain areas of the shelf. They are also of interest to pure mathematicians, studying the eigenvalues of differential operators. Recent analytical and numerical work, using the simplest model possible (unforced, barotropic, rigid-lid approximations) suggests that a number of topographic features (e.g. bays, headlands, submerged valleys or ridges), even bays at lakes ends, can support tCSWs, thus in reality it is a much more common phenomenon than previously thought. The objective of the proposed work is to address a number of open questions regarding the trapping of CSWs, using more complicated models, taking into account the effect of stratification, free-surface, wind forcing and mean currents, by utilising analytical and numerical methodologies. We aim to examine trapping along various shelf-coastline geometries and at lake ends, including stratification and free-surface effects. The physical mechanisms exciting tCSWs will also be addressed, by adding wind forcing and tides into the models. Analytical, asymptotic results will be sought for a weakly curving coast and a straight shelf with weakly curving isobaths, for the stratified, free-surface and wind forcing models using regular asymptotic expansions or a WKBJ method. Numerical pseudospectral methods will be used to validate the asymptotic results and generalise them. These methods are ideal for the non-constant coefficient equations arising from arbitrary stratification and topography, as well as, more complicated models which include the free-surface, wind forcing and mean currents effects.