Abstract

This thesis addresses the observation, analysis and dynamics of waves as being trapped, generated and focused by sloping topography. ---Shelf waves with diurnal tidal frequency off Greenland--- Tidal analysis has been carried out on current measurements at a “cross-shelf” transect off Greenland at 71 N. The diurnal tides manifest themselves
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mainly as a barotropic continental shelf wave, travelling southward along the shelf slope. This follows from the amplitude distribution of the diurnal tidal components and from the rotation sense of the tidal ellipses at different cross-slope locations, as calculated with simple two-dimensional models. The well organized cross-slope pattern of the velocity amplitudes is absent in observations further north near 75 N. These observations suggest that the local vanishing of the group velocity, which is caused by topography, is of importance for the existence and local amplification of these continental shelf waves with diurnal tidal frequency. ---Tidal and residual currents near the shelf break in Biscay--- Internal-wave energy in continuously stratified fluids propagates in the vertical plane, at an angle set by the wave, buoyancy and Coriolis frequencies. Repeated Acoustic Doppler Current Profiler observations on three transects, crossing the shelf edge, now directly reveal this beam-wise propagation of internal tides in the Bay of Biscay. This confirms previous suggestions based on observations sampled more sparsely in space. The present observation is made by bin-wise harmonic analysis of horizontal currents, leading to the spatial resolution of barotropic and baroclinic semi-diurnal tidal and (time-averaged) residual flows. The observed baroclinic tide compares favourably to that produced by a two-dimensional numerical model. The observations reveal details of the internal tidal beam, including its spatial amplitude distribution, presence of amphidromes and direction of phase propagation. The cross-isobath structure of the along-slope barotropic mean flow shows a localized maximum near the shelf break. Over two transects it agrees in sign and magnitude with a theoretical tidally-rectified flow. The baroclinic, cross-isobath mean flow shows a strong near-bottom downwelling flow, compensated by an on-shelf directed flow in the upper part. The along-shelf mean flow displays subsurface-intensification attributed here to frictional modification of a tidally-rectified flow that is bottom-trapped due to stratification. ---Internal wave focusing revisited--- An experiment which discussed the appearance of an internal wave attractor in a uniformly-stratified, free-surface fluid (Maas et al. 1997) is revisited. This is done in order to give a more detailed and more accurate description of the underlying focusing process. Evolution of the attractor can now be quantified. For the tank with one sloping sidewall, and for the parameter regime (density stratification, forcing frequency) studied, the inverse exponential growth rate determined at several locations in the fluid turns out to be 122 seconds always. Only the start and duration of the growth differs: away from the attractor region it appears later and is of shorter duration. Here, these features are interpreted by employing a new theoretical basis that incorporates an external forcing via a surface boundary condition (an infinitesimal barotropic seiche) and that describes the solution in terms of propagating waves.
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