Making more waves: routes to triadic states for internal waves

Abstract

This thesis examines a particular instability of internal waves known as the triadic resonance instability. When this instability occurs, a single internal wavebeam becomes unstable and begins to emit two sibling waves of lower frequency creating a sustained triadic state. Previous work on the linear instability has found that an amplitude threshold for the primary wavebeam must be surpassed before the instability can grow. This thesis investigates whether there are other plausible routes to a sustained triadic response for a system driven by a primary internal wavebeam below this (linear) threshold. Specifically, is there a subcritical bifurcation such that a non-linear disturbance can trigger an instability leading to a triadic state at a lower forcing? And, if so, is this triadic state persistent or only transient? We use laboratory experiments to study whether turbulent three-dimensional flow structures such as vortex rings, bubbles, and plumes – all of which occur in natural flows – can interact with the primary wavebeam and lead to the development of these triadic states. Our analysis of the experimental data includes the development of some new processing methodologies and the application of de-noising methods, dynamic mode decomposition, and sparsity-promoting dynamic mode decomposition for detection of our waves. We find in our results that two routes to triadic states exist for primary waves below the expected amplitude threshold, which we distinguish as transient triadic response (TTR) and sustained triadic response (STR). The type of response provoked appears linked to the amplitude of the primary wavebeam and to the size and location of the perturbation. We also find higher frequency wave—wave interactions that appear to match sums of the triadic waves but not the dispersion relation, making them non-propagating oscillating disturbances that may, nevertheless, affect the longterm behaviour of the propagating triadic waves. These results add up to a more complex picture than previously thought, perhaps indicating wave triads in the ocean have access to more pathways towards energy transfer than currently suggested.