Near-surface interactions between strongly nonlinear internal gravity waves

Lead Research Organisation: University of Cambridge
Department Name: Applied Maths and Theoretical Physics

Abstract

This work will work will focus on the dynamics of internal gravity waves, with particular emphasis on the (nonlinear) interaction between wave beams, the interaction of wave beams with boundaries, the amplification of waves by shear at the surface mixed layer, and the breaking of the waves to generate stratified turbulence. The work will combine a blend of laboratory experimentation (using techniques such as Particle Image Velocimetry, Laser Induced Fluorescence and Synthetic Schlieren), numerical modelling (using Direct Numerical Simulation) and analytical modelling (with techniques ranging from ray tracing and triadic interactions to dimensionality reduction via Dynamic Mode Decomposition and Koopman Modes).

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
NE/R009457/1 01/10/2017 30/09/2022
1946028 Studentship NE/R009457/1 01/10/2017 30/06/2021 Katherine Grayson
 
Description This experimental project has been focused on examining the weakly non-linear instability of internal gravity waves. Internal wave are ubiquitous in the ocean and other stratified media, providing an energy transfer mechanism from the abyssal ocean up the surface. Where these wave break, they deposit energy, resulting in an increasing belief in their ability to contribute to global ocean circulation via energy transport. Understanding their instability mechanisms is therefore of high importance.

We have developed the experimental procedure to examine the breakdown of internal wave beams. We have been utilising a bespoke piece of machinery to generate internal gravity waves from bottom boundary forcing. We have refined the visualisation and measurement techniques, as well as the overall experimental set-up. We designed and built a 'thermal tunnel', which reduces the impact of thermal noise on the visualisation within the experiments. This allows for more accurate measurement of the amplitude of the waves. Currently we have been working with internal waves in a linear stratifications however, by commissioning two new gear pumps, we aim to extend the work to looking at the instability in non-linear stratifications.

We have run experiments looking at the long-term development of the instability, which have previously never been conducted. We have found that the long-term development of instability does not match the current zero-dimensional theory that describes it. The experiments have shown that for a finite width beam, there is significant spatial dependence as to the generation location of the instability and how it evolves in time. We have quantified this experimentally over a range of parameters. We have developed a two-dimensional weakly non-linear model that allows us to capture the spatial and amplitude variation that we are witnessing experimentally. In addition, recent results from the model show that the frequency of the resonant waves does not remain fixed during the instability, rather they fluctuate over time, something also witnessed experimentally.

In addition, we have conducted experiments looking at the interaction of a vortex ring with an internal wave field. A new vortex ring generator was commissioned that enabled us to fire a ring into an existing wave field to examine its breakdown. We found that when the ring collapsed within the internal wave field, the non-linear instability was triggered almost immediately. Further experiments have shown that by introducing a perturbation to the wave field we can trigger the wave to become unstable both at earlier times and at amplitudes lower than the threshold for the instability.
Exploitation Route From our research we hope that there will be greater understanding and clarity on the Triadic Resonance Instability mechanism for internal waves. A greater understanding of these instability mechanisms will help us determine the role of internal waves in their pathway to turbulence and the role they play in ocean mixing.

Also we have greatly developed the experimental ability for generating and examining internal gravity waves in the laboratory. We hope that future users of this experiment will be able to more accurately quantify the effects of mixing generated by internal waves and will be able to undertake more accurate internal wave experiments looking at various phenomena. From the new gear pumps, the ability to look at more oceanic stratifications will be possible, allowing for a more direct comparison of internal wave breakdown within the ocean.
Sectors Aerospace, Defence and Marine,Energy,Environment

 
Description Investigation into multi-frequency internal wave attractors with Felix Beckebanze 
Organisation Utrecht University
Country Netherlands 
Sector Academic/University 
PI Contribution Felix came to Cambridge for a total of 4 weeks, split into two, two week sections. Together, using the apparatus in the GK Batchelor Laboratory in Cambridge, we ran a series of experiments looking at the possibility of hidden internal wave attractors for a multifrequency domain. I helped him with the experimental set up and showed him how to use the specialised equipment in Cambridge. We designed the experimental setup before his arrival and I made sure the experiment was prepared. I helped him with the processing of the experiments and showed him the algorithms we normally use.
Collaborator Contribution Felix was instrumental in analysing the data and writing up the paper from the experiments, which has been submitted to the Journal of Fluid Mechanics but not yet published. He also spent time analysing the data between his visits so that we could tweak the experiments for his second visit and ensure we were getting the most interesting / useful data.
Impact We have submitted a paper to the Journal of Fluid Mechanics with the results from our experiments.
Start Year 2019
 
Description APS Fluid Dynamics Conference Presentation - 2018 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Presentation on experimental results showing the interaction of vortex rings with an internal gravity wave field. First international conference presentation of my work.
Year(s) Of Engagement Activity 2018
 
Description APS Fluid Dynamics Conference Presentation - 2019 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I attended the American Physical Society- Division of Fluid Dynamics- Conference in Seattle. I presented my work on the triadic resonance instability of internal gravity waves to an international academic audience. Afterwards there were some interested questions in my work and I from the session I was able to meet a professor who's work I have been using actively in my own research.
Year(s) Of Engagement Activity 2019
 
Description Presentation at European Geophysical Union 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I took part in the EGU session for internal gravity waves where I gave a short overview of my PhD research. Due to COVID-19, this conference was held online in the form of a chat session with the ability to upload presentations.
Year(s) Of Engagement Activity 2020
 
Description Presentation at the Geophysical and Environmental Processes Seminar 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact This was a 45 minute seminar on my PhD research to members of my faculty and other academics at international institutions. Approximately 35 people were in attendance. Due to COVID-19, this was given in an online format. The talk was well received with many engaging questions and discussion afterwards. The talk was available on the Cambridge University website.
Year(s) Of Engagement Activity 2021
 
Description Presentation at the Waves Special Interest Group (SIG) of the UK Fluids Network. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk on "Interaction of internal gravity waves with a vortex ring" at the Waves Special Interest Group (SIG) of the UK Fluids Network. This was resented at UEA.
Year(s) Of Engagement Activity 2018
 
Description Public Open Day 2019 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Public/other audiences
Results and Impact The GK Batchelor Laboratory plays a pivotal part in the biennial mathematics Open Day. In 2019, there were around 650 members of the public who visited the Laboratory, primarily a mix of family groups. One of the sets of experiments within the Laboratory was specifically motivated by and related to this grant.
Year(s) Of Engagement Activity 2019
 
Description Summer school laboratory assistant 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact During the week long Fluid Dynamics summer school held in Cambridge I was involved in setting up experiments in the laboratory for the students and helping them with their experiments during the day.
Year(s) Of Engagement Activity 2018
 
Description Talk at Norway-Scotland waves symposium 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited talk ("Waves from a magic carpet")
Year(s) Of Engagement Activity 2019
 
Description Talk during Waves SIG at UEA 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk on "Scattering of internal waves by rough topography" at the Waves Special Interest Group (SIG) of the UK Fluids Network.
Year(s) Of Engagement Activity 2018
 
Description University of Auckland: internal waves talk 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact An invited talk within Engineering Science at the University of Auckland
Year(s) Of Engagement Activity 2019
 
Description University of Canterbury: internal waves talk 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited talk within Civil Engineering at the University of Canterbury, New Zeland
Year(s) Of Engagement Activity 2019