Surface Wave Propagation using Ray Optics with Applications to Hamilton Harbour

Abstract

Surface gravity waves are a commonly observed phenomenon in closed lakes. They are primarily generated by winds, but may also be generated by wakes of vessels in the water or tidal forces. These waves are known to undergo refraction and changes in energy (and therefore, amplitude and speed) as they propagate over variable depths in a closed lake. In this thesis, we use the linearized ray optics equations to study the propagation of surface waves in closed lakes with variable bathymetry. We assume that the fluid is inviscid, irrotational and incompressible. We further assume that the wavelength of these waves is much smaller than the length scales over which bathymetry (depth) varies – in other words, we assume the waves propagate in a slowly varying environment. We perform a series of numerical simulations of surface wave propagation with various initial conditions and bathymetries to validate the model, as well as gain insights on the effects of roughness of the bathymetry in diverting the expected trajectories of these waves. Finally, we present a case study on Hamilton Harbour. This watershed has been under scrutiny for several years due to rising eutrophication levels affecting the dissolved oxygen levels in the basin. We apply the numerical model to the bathymetry of Hamilton Harbour to locate hotspots of wave accumulation in the lake, which may provide inference of regions in the lake where we expect sediment resuspension which is one of the primary factors of internal loading of phosphorus in lakes.