Turbulent mixing across zero-mean flow density interfaces
Lead Research Organisation:
University of Cambridge
Department Name: Applied Maths and Theoretical Physics
Abstract
This project will explore mixing across a density interface driven by high-Reynolds number turbulent flows in contexts where there is zero mean flow in either layer. While this is a classical problem, it is one that remains poorly understood and it is timely to look afresh and make use of recent experimental, numerical and theoretical developments. The research will employ the near-instantaneous 3D velocity and density diagnostic capability pioneered in DAMTP during the last year, and couple this directly with high-resolution Direct Numerical Simulations to probe realisable states of the turbulent field. Theoretical developments will draw on recent ideas such as Koopman modes and unsteady period orbits to probe the structure and dynamics of the turbulence.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509620/1 | 01/10/2016 | 30/09/2022 | |||
| 1781795 | Studentship | EP/N509620/1 | 01/10/2016 | 30/09/2020 | Benjamin Jackson |
| Description | This project explores the dynamics and mixing properties of vortex rings that impact the density interface of a two-layer density stratification in a stationary environment. Vortex rings can be thought of as highly reproducible balls of kinetic energy that efficiently self-propagate, making them an ideal candidate for studying experimentally the behaviour of eddy-like structures in turbulent flows. Our work extends an almost 50 year old analogy between vortex rings and turbulent eddies mixing at density interfaces, by investigating the effect the impact angle has on the ring-induced mixing that ensues. To obtain velocity measurements in experiments, PIV (Particle Image Velocimetry) is used. Traditional PIV compares pairs of particle images that are a fixed interval in time apart. This technique has a limited dynamic velocity range for which accurate velocity measurements can be made, smaller than the range of velocities exhibited in a typical vortex ring-interface interaction. To overcome this constraint, we developed a modification of the traditional PIV technique that allows for accurate velocity measurements to be made for all velocity scales exhibited in our experiments. Prior to this project, the internal dynamics of a ring obliquely impacting a density interface had not been explored. Using our PIV algorithm in conjunction with LIF measurements to obtain velocity and density measurements, we have investigated the evolution of the ring-interface interaction for a range of impact angles and stratification strengths. These observations have shed light on how the varying the impact angle will affect the mixing efficiency of the rings, and more broadly how vortical structures might behave at a sharp density stratification. For near-vertical impact angles and strong stratifications, we have carried out experiments to determine the mixing efficiency of vortex rings. These measurements are obtained by periodically generating vortex rings in an initially two-layer stratification and measuring 1D profiles of the evolving density stratification. For the range of parameters considered, our experiments indicate that vertically propagating rings have the highest mixing efficiency. This appears consistent with the modification we have made to a pre-existing analytical model for ring-induced mixing, which allows the choice of impact angle to be incorporated into the model. We are in the process of numerically solving this model to validate our experimental results. We have yet to conduct similar mixing efficiency experiments for vortex rings mixing a weak two-layer stratification. We plan to conduct these experiments soon. |
| Exploitation Route | We have extended the vortex ring-eddy analogy to study the influence of localised coherent structures in mixing a stratification. In the geophysical context, regions of turbulence are much more complex than the idealised case we have investigated. There are other idealised flows that can say something meaningful about the role of vortical structures in stratified turbulent flows. Relatively simple examples include a vortex pair obliquely impacting a density interface, the head-on collision of two obliquely propagating vortex rings which meet at a density interface, and an inclined oscillating grid that mixes a two-layer stratification. Our observations and results may provide insights on the dynamics of such flows. The PIV algorithm we have developed could also be used to effectively extract velocity data in future experiments where the dynamic velocity range of the flow exceeds the dynamic velocity range that traditional PIV methods can capture. |
| Sectors | Environment |
| Title | Filling tank apparatus |
| Description | I chose the category above in the preceding question as it seemed quite broad/wide ranging, and all the other options were related to biology or chemistry. We developed new apparatus that considerably reduces the total filling time of our tank when creating a two-layer stratification. The apparatus allows for a relatively large volume flux to go into the tank whilst ensuring that any turbulent kinetic energy diffuses so as to not mix the density interface as the tank is filled for an experiment. In particular, it now takes about 40 minutes to fill our lower layer of our stratification, whereas the previous method employed would have taken around 5 hours. |
| Type Of Material | Improvements to research infrastructure |
| Year Produced | 2017 |
| Provided To Others? | No |
| Impact | This was vital in allowing us to make accurate PIV measurements near the density interface for the range of parameters we are investigating in our experiments. Prior to this development, the tracer particles used to make PIV measurements would gather towards the interface, creating a "cloud" of particles. This made it difficult to observe any of the interesting dynamics using the PIV technique. With the new filling technique this issue no longer poses a problem. Reducing the total filling time also limits the effects of diffusion before the experiment is initialised. |
| Title | Modification of traditional 2D PIV |
| Description | I chose the category above in the preceding question as it seemed quite broad/wide ranging, and all the other options were related to biology or chemistry. To obtain velocity measurements in experiments, PIV (Particle Image Velocimetry) is used. Traditional PIV compares pairs of particle images that are a fixed interval in time apart, in order to make velocity measurements. This technique has a limited dynamic velocity range for which accurate velocity measurements can be made, smaller than the range of velocities exhibited in a typical vortex ring-interface interaction. We developed a modification of the traditional PIV technique that interrogates image pairs of different intervals in time apart, and overlaying these measurements onto a single velocity output. Though versions of this method have been developed before, our algorithm aims to minimise the number of local interrogations that need to be made (thus reducing the total computational time), and our weighting criteria has been developed to cope with the limited ability of interrogating the flow at the smallest time steps we can utilise. |
| Type Of Material | Improvements to research infrastructure |
| Year Produced | 2019 |
| Provided To Others? | No |
| Impact | This method allows us to analyse the flow with greater clarity, as structures of all the velocity scales (of interest to us) in the flow can now easily be observed (as opposed to being obscured by noise). This is particularly important for our experiment as often a wide range of velocity scales are exhibited in our flow at a given instance in time. |
| Description | American Physical Society, Division of Fluid Dynamics 2019 Conference |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | 10 minute presentation on how the mixing properties of a vortex ring impacting a density interface is influenced by the ring propagation angle. The talk was well received, and there were many questions from audience members. The talk led to an extended one-to-one discussion with a current PhD student in Toulouse, working on a related but different problem. |
| Year(s) Of Engagement Activity | 2019 |
| Description | CISM Summer School |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Lecturing (6 hours) in an international Summer School on Turbulent Mixing in Stratified Flows held at the Centre International des Sciences Mecaniques in Udine, Italy. |
| Year(s) Of Engagement Activity | 2018 |
| Description | Mathematics public open day |
| 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 Centre for Mathematical Sciences (CMS) has an annual public open day, in which the GKB Laboratory (fluids lab) is opened up to the public every other year. The intention of the open day is to engage and enthuse the general public about mathematics in general. For the 2017 open day I volunteered in the fluids lab, demonstrating and explaining experiments to the general audience. I will also be doing this again for the 2019 open day (taking place March 23rd). For the 2017 open day, (I believe) approximately 700 people came to visit the fluids lab. Members of the public were engaged and interested in the range of experiments that were demonstrated, and many were eager to learn more. |
| Year(s) Of Engagement Activity | 2017,2019 |
| 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 |
| 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 | Around 45-50 postgraduate students attended a two week summer school at my research department, in which I volunteered as a helper. This mainly involved assisting summer school students in their lab workshops. One of the lab projects was a creative art project, for which I did a significant amount of work in developing a user friendly interface allowing both the summer school students to use the equipment and software, as well as the artists who did not have a scientific background. The students attending the summer school were engaged and enthused by the various experiments and workshops they worked on as part of their summer school, and many interesting discussions were had. |
| Year(s) Of Engagement Activity | 2018 |
| Description | Talk at Turbulent Mixing and Ejecta at Interfaces, April 2019 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Public/other audiences |
| Results and Impact | Invited talk at meeting co-organised by CEA and AWE. Meeting in Cambridge, April 2019: "Workshop meeting on turbulent mixing and ejecta at interfaces". Participants from CEA, AWE and academia. |
| Year(s) Of Engagement Activity | 2019 |