The refraction, shoaling and structure of non-linear internal waves at a continental shelf margin
Observations of internal waves near the Continental shelf-edge are generally ascribed to generation by oscillating tidal flow over the local bathymetry, in the presence of a stratified water column, giving rise to the internal tide. In this thesis observations are presented which demonstrate that internal waves at the Malin shelf-edge comprise of both the locally generated internal tide, and waves from a distant source. This thesis focuses on processes affecting the latter phenomenon at the continental slope. A comprehensive collection of in-situ and satellite data from the Shelf Edge Study (SES) and the Shelf Edge Study Acoustic Measurement Experiment (SESAME) from August-September 1995 and August 1996 is used to describe the internal wave characteristics. During a period of neap tides a set of internal solitary waves was tracked across the continental slope every tidal cycle for three days. The measurements indicate that the waves evolved from an initial drop in the thermocline, and were not significantly refracted as they crossed the slope, due to the small change in phase speed across the slope, from around 0.8 to 0.6 ms"1. The internal waves depressed the thermocline by between 30 and 50 m and had particle speeds of 0.4 to 0.8 ms"1. The structure of the internal waves is examined and compared to weakly non-linear theory, and it is found that first order theory adequately describes the waves over the slope but that a second order theory is required to model the internal waves on the shelf. A non-linear refraction model is developed to simulate the internal wave propagation and evolution. Initial tests of the model for the refraction and shoaling of interfacial solitary waves propagating in simple environments show agreement with analytical results. The model is then extended to simulate the refraction and transformation of the internal waves observed during SES, using realistic density stratification and bathymetry. When realistic initial conditions derived from measurements are used, it is found that the model reproduces the phase speeds and refraction characteristics very well, but overestimates wave amplitudes at the shelf-edge and the shelf. Analysis of the simulated internal waves suggests that the waves would become unstable at these amplitudes and would in reality be damped. In fact it is shown from the observations that instabilities in the wave are likely to occur due to the high shear and high particle speed relative to the phase speed, and an example of possible breaking internal waves is illustrated. The likely regions of non-linear internal wave dissipation are considered in the Discussion, together with the local generation of internal tides, and possible source regions for the distant internal waves.