Nonlinear Interactions of Internal Gravity Waves

  • Tom Dobra

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Internal waves carry more available energy than any other transmission system on Earth: lunar diurnal excitation drives 1 TW of wave power inside the world's oceans. Energy is transmitted over thousands of kilometres and individual waves may be hundreds of metres high. Where they break, they deposit their energy, and, in such regions, they greatly enhance the vertical transport of carbon dioxide, oxygen and heat. Despite their significance, much remains to be understood about internal waves, and this thesis explores some of these questions using a combination of experiments and theory. One way to generate internal waves is by sinusoidally oscillating the boundary of the fluid. A full spectrum of harmonics is generated, whose phases and amplitudes are predicted by perturbation theory. Their origin is identified solely as nonlinear geometric excitation at the boundary; no interactions between the harmonics of the same infinitely wide, monochromatic input are possible within the fluid. However, for narrow wave beams, resonant triadic wave-wave interactions are predicted using a novel numerical implementation of the singular two-dimensional Green's function. To verify the predictions, a new experiment was designed, consisting of an electronically actuated "magic carpet" inserted into the base of a tank. It perturbs the fluid lying above its surface to generate internal waves of almost any shape and size. The carpet is actuated by an array of 100 stepper motors, which are controlled by bespoke software that manages the timing in increments of 30 ns; this ensures precise spatiotemporal control of the waveform. The carpet itself is made of a neoprene-nylon composite, and its bending behaviour is modelled in detail to characterise the waveform imparted on the fluid. The experiments support the theoretical predictions, but also permit strongly nonlinear regimes, such as wave breaking, at amplitudes above the applicable domain of the theory.
Date of Award23 Jan 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorAndrew G W Lawrie (Supervisor) & S B Dalziel (Supervisor)

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