Internal wave patterns in enclosed density-stratified and rotating fluids

Abstract

Stratified fluids support internal waves, which propagate obliquely through the fluid. The angle with respectto the stratification direction is contrained: it is purely determined by the wave frequency and the strength of the density stratification (internal gravity waves) or the rotation rate (inertial waves). As a consequence, when these waves reflect from a sloping wall, they are focused or defocused, depending on their direction of incidence. Repeated reflection with focusing in an enclosed basin may lead to the appearance of a wave attractor, a limit cycle to which all wave rays converge. Contrary to standing waves, which exist for isolated frequencies, wave attractors exist over frequency intervals . Internal waves are observed in the ocean and are possibly relevant for the liquid outer core of the Earth and stars. When energy becomes concentrated along the attractor, part of it may become available for mixing and eventually for the generation of a mean flow. This is important for transport of nutrients and sediments in the ocean, and ultimately also for the maintenance of the global ocean circulation. In chapter 2 of this thesis, the role of the (two-dimensional) basin shape is investigated theoretically. A completely smooth geometry was investigated, which varies between a circle (no attractors possible) and a triangle (vertices act as point attractors), depending on a parameter. Attractors were indeed found. First order perturbation analysis revealed that attractors may arise for the weakly perturbed circle. So corners or critical latitude singularities are not essential for the existence of attractors. In chapters 3 and 4 inertial waves in a homogeneous fluid were investigated experimentally. A rectangular basin with one sloping side wall was placed on a rotating platform, of which the rotation frequency was modulated to generate inertial waves. Waves of different frequencies were used to observe different wave attractors. Predicted wave attactors were indeed observed, but with intensity and phase changes in the horizontal direction, different for the different frequencies. In chapter 3, emphasis is on the observation of different wave attractors and changes in their structure in vertical cross sections of the basin. In chapter 4, a smaller tank is used to resolve the horizontal structure of the wave field better, and the (necessarily) three-dimensional wave field is discussed in more detail. In chapter 5 internal tides were studied in the Mozambique Channel, a sea strait of about 350 km wide and 2.5 km deep. An array of current meters had been deployed for more than a year and a half. The internal tides appeared highly variable (intermittent) but, regarding a large period of observation, regions of stronger and weaker motion could be identified. Results were compared with those of a numerical internal-tide generation model. Qualitative agreement was found, especially regarding the strong motion in the upper part of the water column. This is an effect of the strong change in stratification (pycnocline). But also in the deep-sea, areas with stronger and weaker motion were identified. Wave attractors could not be identified. But the observed and numerically predicted spatial changes in the internal tide strength can be partly understood by considering repeated reflection of internal waves in enclosed basins.