- Internal waves and tides are a dominant source of current variability, and they are intermittent and hard to predict. Internal waves can have significant variability in alongshore structure. However, previous studies on internal waves have focused primarily on their cross-shore structure and propagation. For example, while alongshore-propagating superinertial internal tides are known to exist in the ocean, their dynamics are not well understood. This dissertation entails two research directions that address different aspects of along- (and cross-) shore properties of internal waves, focusing on understanding alongshore variability of internal waves and tides and mechanisms that cause it. In one (Chapter 2), observations from seafloor pressure sensors and linear theory are used to investigate along- and cross-shore structure of high-frequency nonlinear internal waves. In the other (Chapters 3 and 4), linear theory is used to investigate excitation of coupled barotropic-baroclinic resonant modes in idealized basins and their application to understanding coastal and basin internal tide dynamics and intermittency.
In Chapter 2, along- and cross-shore variability in propagation speed, direction, and kinetic energy of packets of high-frequency nonlinear internal waves in Massachusetts Bay are investigated using a two-dimensional array of seafloor pressure sensors and linear theory. This region is known for the predictable occurrence of these wave packets, making it a good location to test the utility of using an array of low-cost pressure sensors to study high-frequency internal waves. Speed and direction are determined using only the pressure sensors, and their alongshore variability is quantified. Linear theory predicts a relationship between kinetic energy and bottom pressure variance that is sensitive to sheared background currents, water depth, and stratification. Comparisons with seafloor acoustic Doppler current profiler measurements nonetheless show a strong relationship between kinetic energy and bottom pressure variance. This is presumably due to phase locking of the wave packets to the internal tide that dominates background currents and to horizontally uniform and relatively constant stratification throughout the study. Thus the observed bottom pressure variance is used to qualitatively describe variations in wave packet kinetic energy.
In Chapter 3, linear theory for idealized two-layered basins with a free surface and alongshore uniform shelves is used to investigate effects of basin size, continental shelves, shelf-deep phase speed ratio, and rotation on coupled barotropic-baroclinic superinertial resonant modes. Large amplitude coupled barotropic-baroclinic basin modes, shelf-amplified basin modes, and edge modes are excited by a body force, modeled as an idealized equilibrium tide. Shelves are shown to have a strong effect on basin modes once the shelf width is greater than a quarter-wavelength of a mode. The phase speed ratio over the shelf versus deep basin is important in determining how much mode structures will be affected by shelves. The smaller the ratio, the more separation between scales of shelf and deep responses, resulting in more edge modes for a given frequency range and edge modes that decay faster into the deep basin. Full basin mode excitation requires a basin to reach equilibrium, but time scales over which stratification and thus basin mode structure change could be shorter than baroclinic adjustment times. Therefore, in the real ocean, basin modes for barotropic tides could occur in large basins, due to their relatively fast phase speeds, but slower propagating baroclinic tides would only be able to develop full basin modes in smaller basins. Shelf-trapped edge modes depend only on the shelf geometry, and not that of the deep basin, so baroclinic edge modes can develop much more quickly, making them possible for any continental shelf with the appropriately tuned geometry. In rotating basins, baroclinic edge modes can have phase that propagates alongshore (in either direction) or a complicated phase and amplitude structure that results in what appears more like standing waves. These findings indicate that shelves and shelf-deep phase speed ratios can have a significant impact on the structure of barotropic and baroclinic tides, that resonant mode excitation can generate large-amplitude shelf-trapped superinertial internal tides, and that some temporal variability of internal tides could be explained by stratification tuning toward and away from resonance.
Building on this, in Chapter 4, alongshore shelf width variability is introduced to the idealized basins. In nature, continental shelves are not perfectly uniform alongshore, so these simulations are performed to understand what might happen with resonant modes in the real ocean. A small phase speed ratio over the shelf versus deep basin is used to focus on responses over the shelf. The shelf is on the western boundary of the basin, and is narrow to the north and south, with a wide middle section. Some resonant edge modes have large amplitudes isolated to the wide section of the shelf, some have large amplitudes along the entire shelf, but more confined to the narrow width extent, and some have large amplitudes distributed over the entire shelf. Alongshelf and cross-shelf wavelength scales in a resonant response can be different for the narrow versus wide sections of shelf, as can sense of phase propagation. These results indicate that large-amplitude superinertial internal tides from resonant edge modes can occur on realistic continental shelves of ocean basins, with resonance being associated with smaller segments of a shelf and not needing to communicate with the entire alongshelf distance of a basin. This could account for some observations of alongshelf variability in superinertial internal tides.