Scattering of internal gravity waves

Abstract

Internal gravity waves play a fundamental role in the dynamics of stably stratified regions of the atmosphere and ocean. In addition to the radiation of momentum and energy remote from generation sites, internal waves drive vertical transport of heat and mass through the ocean by wave breaking and the mixing subsequently produced. Identifying regions where internal gravity waves contribute to ocean mixing and quantifying this mixing are therefore important for accurate climate and weather predictions. Field studies report significantly enhanced measurements of turbulence near ‘rough’ ocean topography compared with those recorded in the ocean interior or near more gradually varying topography (e.g. Toole et al. 1997, J. Geophys. Res. 102). Such observations suggest that interaction of waves with rough topography may act to skew wave energy spectra to high wavenumbers and hence promote wave breaking and fluid mixing. This thesis examines the high wavenumber scatter and spatial partitioning of wave energy at ‘rough’ topography containing features that are of similar scales to those characterising incident waves. The research presented here includes laboratory experiments using synthetic schlieren and PIV to visualise two-dimensional wavefields produced by small amplitude oscillations of cylinders within linear salt-water stratifications. Interactions of wavefields with planar slopes and smoothly varying sinusoidal topography are compared with those with square-wave, sawtooth and pseudo knife-edge profiles, which have discontinuous slopes. Far-field structures of scattered wavefields are compared with linear analytical models. Scatter to high wavenumbers is found to be controlled predominantly by the relative slopes and characterising length scales of the incident wavefield and topography, as well as the shape and aspect ratio of the topographic profile. Wave energy becomes highly focused and the spectra skewed to higher wavenumbers by ‘critical’ regions, where the topographic slope is comparable with the slope of the incident wave energy vector, and at sharp corners, where topographic slope is not defined. Contrary to linear geometric ray tracing predictions (Longuet-Higgins 1969, J. Fluid Mech. 37), a significant back-scattered field can be achieved in near-critical conditions as well as a forward scattered wavefield in supercritical conditions, where the slope of the boundary is steeper than that of the incident wave. Results suggest that interaction with rough benthic topography could efficiently convert wave energy to higher wavenumbers and promote fluid mixing in such ocean regions.