Mathematical underpinnings of stratified turbulence

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

Abstract

Turbulence is an everyday experience, from the water emerging from a tap to the wind on one's face. Despite its widespread importance, a mathematical description of turbulent flow remains elusive. In most turbulent flows of practical interest, the vast number of degrees of freedom makes it impossible to solve the equations of motion directly. Recently, however, significant progress has been made by taking the view point that turbulence can be treated as a large dynamical system in which the turbulence is represented by differential equations that, in principle, can be integrated forward in time to evolve from one state to the next. While previous work in this area has focused on uniform density fluids, the buoyancy forces associated with density variations play an important dynamical role in many applications (e.g. warm air is less dense than cold air, which is critical for efficient building heating and cooling strategies).

This project will develop the mathematical underpinnings of stratified turbulence. The project builds on the dynamical systems viewpoint, developed for a fluid which has a constant density and extends it to one in which the fluid density varies in space and time. In addition to extending the analysis to new practical applications, including buoyancy effects associated with density variations will allow us to probe universal aspects of turbulence in a way that would not be possible in a homogeneous fluid. Much of the progress in turbulence theory to date has been in flows which are transitional so the flow is in an intermediate state between being completely laminar and completely turbulent. In a stratified fluid, the buoyancy force inhibits vertical motions (e.g. warm air tends to stay near the ceiling) and makes laminar/turbulent transitions more prevalent, their structures more identifiable, and the dynamics richer so there are more phenomena to explore.

Our approach is based on tight coupling between mathematics, simulation and experimentation. Although stratified turbulence has been studied experimentally for many years, none of the existing flow geometries can address all three of our primary objectives. Consequently, we will build a new experiment to study stratified turbulence in a canonical geometry in which the turbulence is generated by shear and opposed by the stratification. This new geometry will allow us to observe and measure laminar/turbulent transitions, the flow structures that are involved and their distributions in time and space. We will also carry out new experiments in two other geometries to examine how the flow features change in different configurations. We will use numerical simulations of each experimental configuration to complement the laboratory experiments by allowing additional diagnostics, and providing a direct link between the mathematical tools and the flow geometries.

One of the important outcomes of combining mathematical analysis, laboratory experiments and numerical simulations will be to develop a simplified dynamical description of the system. This reduced dynamical system will capture the key physics of stratified turbulence, and provide a generic tool for understanding and modelling turbulence and mixing processes in diverse contexts of economic, environmental and societal importance. Eventually we hope to provide practical estimates of mixing and transport in a turbulent stratified fluid.

Planned Impact

Stratified turbulence inevitably leads to irreversible mixing of the stratifying agent. Any industrial process involving fluid connects with this research if the fluid either contains different concentrations of scalars or varies in temperature. We give three examples to illustrate the likely beneficiaries of this research, all of which have a potential significant impact on the nation's economy.

1. Architects, designers and structural engineers. In the drive for low-energy (or zero-energy) buildings there is a demand for new methods of heating and cooling. These often involve hybrid (or mixed-mode) approaches that combine mechanical cooling and natural ventilation, and inevitably lead to flow and mixing of air of different temperatures and different pollutant concentrations. Estimates of mixing rates are critical to ventilation efficiency and energy consumption, indoor air quality and perceived comfort. Designers use software in which these mixing processes are ignored or represented in simplified inaccurate forms. The outcomes of our research will provide accurate estimates of mixing rates related to the ventilation flows that can be implemented into design codes. Such issues are often critical to conservation of artwork, or in heritage buildings (e.g. museums).

2. Engineers in the hydrocarbon and related industries. Most industrial fluids are mixtures with components of different densities (often different phases). Transporting such fluids in pipelines typically induces turbulence and shearing flows with many features in common with the flows we are considering. Coherent flow structures of the kind we will identify will be present in these practical situations with consequences for wear, corrosion and/or deposition within pipes. The results of our research will provide guidance on the properties of the coherent structures by identifying the circumstances under which they might occur and ultimately mitigating their unwanted effects. There are also many circumstances in chemical processing where thorough mixing is desired, and our research should point towards ways to enhance mixing in the presence of density gradients. Furthermore, our approach of solving technical challenges through a tightly-coupled and inter-related experimental, numerical and mathematical effort can serve as an exemplar.

3. Climate scientists, oceanographers and meteorologists. Irreversible mixing processes in the oceans and atmosphere take place on very small length and time scales (a few cm and seconds) that are far beyond the spatial and temporal resolution of even the most highly-resolved numerical weather forecast models. Consequently, they are parametrised by approximate models that relate these processes to the larger-scale resolved fields. The outcome of our research will provide new insights into the dynamics and new mathematical representations that will lead to improved parametrisations.

The scale of these impacts is potentially very large. Hydrocarbons are the largest component of global energy supply. Buildings contribute about 30% of the UK's carbon emissions and more energy-efficient ventilation will reduce that significantly. Similarly, improvements in weather and climate predictions have immense economic benefits. We expect that some of these impacts will be realised within the next 10 years. Demand reduction in the built environment is a hot topic and there are an increasing number of architects who claim 'green' credentials, some using the results of our work published over the last 20 years, and the general public will benefit from reduced energy bills. We also expect our work to guide the development of new parameterisations for climate models.

The staff working on the project will gain a wide range of skills including computational and laboratory expertise, team working, presentational skills and interpersonal skills.

Publications

10 25 50
 
Description The overarching goal of this research was to develop the mathematics necessary to increase our understanding of the dynamics of turbulence in stratified fluids as an exemplar of a system with spatiotemporal complexity. To approach this goal, we had the following four specific research objectives.

Objective 1
To develop new mathematical tools, based on a dynamical systems approach, to establish the mathematical structures that underpin the dynamics of turbulence in a stratified fluid. In pursuit of this objective we aim to:
(a) Identify coherent structures (simple invariant solutions of the system, typically unstable periodic orbits, usually localised) and track their important manifolds.
(b) Explore transition by extending recently developed tools of edge-tracking and minimal seeds to spatially extended domains.
(c) Examine spatio-temporal intermittency through the structure of the laminar-turbulent interface, and the connection to coherent structures, wave radiation and transition.

Key findings
For (a), we decided to look first at small-domain plane Couette flow (fluid confined between two parallel walls moving differentially) at low Reynolds numbers to examine how the presence of stratification parallel to the shear modifies known coherent structures [32]. Three regimes were found with stratification having a strong suppressing effect. This work was initially performed at a Prandtl number of 1 but recent work [49] has looked at varying this with high Prandtl number of particular interest given other results obtained during the course of the grant (e.g. [20]). In this limit, the coherent structure adopts a well-mixed interior sandwiched between strongly stably stratified layers which resonates with what is seen in stratified turbulence. Shear with now perpendicular stratification (e.g. horizontal plane Couette flow) was also studied [28, 29, 41] with one particular success being the identification of layering as a consequence of coherent structures connected directed to a linear instability mechanism [28]. The mixing efficiency of some of these coherent structures was also studied and compared to turbulent values [28]. We also examined localization mechanisms in these flows and developed a new variational technique to track unstable manifolds leading to turbulence from coherent structures on the laminar-turbulent boundary [33].

(b) A variety of techniques have been used to probe the key active dynamics at the laminar-turbulent boundary in stably-stratified shear flows. For example: minimal seed calculations were done in [8] to probe how stratification modified the minimal seed and edge state; direct numerical simulations in [5, 42] uncovered the different mechanisms responsible for relaminarisation when the stratification is parallel with, or perpendicular to, the shear; edge-tracking in [36] attempted to isolate localized stratified coherent structures; and transient growth analysis in [2,24] was used to probe for finite-amplitude instabilities. One particularly notable success here has been the development of a control technique to stabilize turbulent spots [15]. Work is continuing to develop tools based on Dynamic Mode Decomposition and Koopman analysis to study these spots [43, 44]. The plan is also to use these tools to analyse transient mixing processes to extract the key processes involved.

(c) The main progress in examining spatio-temporal intermittency has been experimental (see description of the SID experiment under 2. below) and numerical (see [5, 28, 42] and the discussion under 3. below ). Considerable theoretical progress has been made linking the coherent structures seen in the SID experiment with a simple stability analysis of the measured mean flow [36]. There is plenty more to do here in matching observations with simulations. The main challenge currently being tackled is to develop a more accurate numerical model of the experiment with the hope that the large amount of data collected can be used to initiate simulations directly. As mentioned in b), the ability to control turbulent spots [15] so they neither grow nor decay has opened up a considerable opportunity to look for the signatures of simpler coherent structures in this localized turbulence.

A particular area of interest in stratified turbulence is the coupling between turbulent motions and internal wave fields, of particular geophysical and military interest [7], [9], [30]. The developed understanding of turbulence in plane Couette flow, particularly when the density gradient and shear are orthogonal [38] suggests it will now be possible to consider such coupling in a very highly controlled and constrained flow geometry.


Objective 2
To conduct laboratory experiments on three different flow configurations to examine (a), (b) and (c) above and to provide data to inform the numerical solutions of the governing equations and test the results. To achieve this we aimed to:
(a) Develop a new canonical experiment on stratified plane Couette flow to examine the interaction of vertical shear and vertical stratification, and the relative effects of internal and external mixing.
(b) Study stratified turbulence in the absence of mean shear and mean flow in a stratified mixing box.
(c) Investigate the effects of mean flow and the roles of layering and interfaces in turbulent mixing in a stratified Taylor-Couette flow.

Key findings
We decided on the basis of early numerical computations that it is impossible to establish a strongly stratified turbulent plane Couette flow since the stabilizing fluxes at the boundaries suppress the development of turbulence in the interior [5]. We also found that the stratified mixing box, which was intended as a back-up experiment, was not as informative as we had expected. Instead we developed a new experiment - the stratified inclined duct (SID) - and concentrated particularly on that and the stratified Taylor-Couette (STC) experiment.

SID is a canonical new experiment in that it is highly versatile and provides a maintained stratified shear flow at high buoyancy Reynolds numbers, both features of natural and industrial stratified flows. We have developed new diagnostics that allow, for the first time, combined measurements of all three components of velocity and the scalar field over a three-dimensional volume. These new diagnostic capabilities required the development of new bespoke hardware and software that are significantly in advance of current commercially available products [40]. Our approach, combining two levels of scanning, provides very-high-resolution high-fidelity and near-instantaneous time-resolved measurements across an extended volume. For the SID geometry we have been using, we have been able to get a resolution close to the Kolmogorov scale at high enough Reynolds numbers for the flow to be turbulent, and have mapped out a path to increase both the spatial and temporal resolution further in a new version of SID under construction (supported by an ERC grant awarded to the PI).

The stratified inclined duct has proved to be a very effective experiment that demonstrates the spatio-temporal intermittency that lies at the heart of the project [1]. We discovered that it exhibits four different flow regimes: laminar, Holmboe, intermittent and turbulent. We used our innovative flow diagnostics to explore the structures in the different flow regimes. We found that the Holmboe regime results from an intrinsic three-dimensional linear instability of the experimentally measured flow that provides resilient structures that persist at finite amplitude [36]. We found, however, that these nonlinear waves contribute little to the energetics of the flow, which for this regime is dominated by the boundary layer dissipation. A modified form of these structures persist into the intermittent and turbulent regimes [41], and are responsible for the three-dimensional dissipation at higher Reynolds numbers. Thus we have identified structures as in Objective 1(a) and explored their dependence on the overall flow parameters [33]. We have explored them in transition (Objective 1(b)) and in the intermittent state (Objective 1(c)). We also explored the transitions between the different flow regimes and identified the parameter that governs each regime. This, in turn, has important implications for the energy balances in each case.

A further unanticipated result is that by conducting experiments in SID with thermal (rather than solutal) stratification showed that the flow regimes depend on the Peclet number of the flow. This was also investigated numerically, where we found that sharp interfaces could only be maintained for large values of the Peclet number [23, 24].

Extensive experiments have also been conducted in the stratified Taylor-Couette flow geometry, considering two particular flow states: initially linearly stratified, and initially two-layered stratification. When the background stratification is initially linearly stratified, (as noted in the original proposal) the stratification spontaneously forms a layer-interface structure, with relatively deep well-mixed layers separated by apparently robust, yet thin, strongly stratified interfaces. However, we have discovered that these interfaces are actually spatio-temporally intermittent, with mixing events quasi-periodically disrupting the interfaces, which then reform. Furthermore, there appears to be a characteristic phase-shift between these mixing events on neighbouring interfaces. This characteristic phase-shift suggests the possibility that the initial imprint is associated with helical instability modes, commonly referred to as the "strato-rotational instability" (SRI) as we have demonstrated through a combination of stability analyses, simulation and experiment.

In the second situation, when the initial stratification is two-layered with a single interface, we have been able to conduct a detailed experimental analysis of the quasi-periodic mixing event that also appears in this flow, suggesting that the mixing event is inherently nonlinear and not reliant on the inherently helical SRI. Through coupled velocity and scalar field measurements, we have identified the key role played by a coupled combination of ejections from the boundary layers at the inner cylinder and associated "sharpening" of the density interface for the development and maintenance of this mode-1, extremely robust coherent mixing structure.

Although, as noted above, we did not pursue the stratified mixing box experiment to any depth, we did pursue a closely related experiment, namely vortex ring mixing (VRM). In this experiment, rather than considering a general turbulent field, we explored in detail the mixing generated by the impingement of a vortex ring on a density interface, considering a vortex ring as an archetype of the vortical structures that drive the mixing in the turbulent case. This work both revealed a much higher mixing efficiency than has previously been recognized for such interactions [6] and explored the role of primary and secondary instabilities in providing the mixing mechanism [30]. Pursuing the latter also provided a stepping-stone towards the development of our new diagnostics.

Objective 3
To carry out advanced computations to solve the governing partial differential equations and simulate the experiments in a manner that aims to:
(a) Provide accurate direct numerical simulations of stratified turbulence to act as the foundation for the mathematical analysis by extracting the dynamical structures such as the relevant unstable periodic orbits, localised invariant solutions and tracking manifolds, and by determining the form of the laminar-turbulent interfaces and the minimal disturbances that initiate transition.
(b) Use high resolution numerical simulations of the three flow configurations to complement the laboratory experiments by providing additional diagnostics.

Key findings
We started our numerical efforts focused on Direct Numerical Simulations (DNS) of stratified plane Couette flow. In this geometry we found fully turbulent, laminar, and spatio-temporally intermittent flow depending on important non-dimensional flow parameters [5]. Our early simulations (and indeed most of the existing numerical simulations of stratified turbulence) used a relatively small Prandtl number, appropriate for thermally stratified air. In order to bridge the gap between these simulations and the salt-stratified experiments in water, we explored the sensitivity of the turbulent flow to the Prandtl number [21]. We found that the Prandtl number (or more appropriately the Peclet number) strongly modifies the stratification effects - supporting the conclusion reached based on the laboratory experiments with heat and salt stratified water mentioned above in 2.

One of our central aims was to examine the spontaneous development of layers and interfaces in stratified turbulence. We developed a new theory to describe the necessary condition for spontaneous layer formation in stratified shear flows [24] and applied this theory to simulations of stratified plane Couette flow [23]. We found that for sufficiently large Peclet and Richardson numbers, it was possible for the flow to maintain a stratified interface.

Another of our central aims was to study the coherent structures that exist at the interface between turbulent and laminar flow in a stratified fluid. We developed a new technique for isolating these structures in numerical simulations [15]. We found that the intermittent turbulent structures in stratified plane-Couette flow take the form of stripes and spots. The structure with the lowest energy level that we were able to isolate using this method took the form of a single coherent and persistent turbulent spot, surrounded by otherwise laminar flow. We speculated that this structure might represent the `minimal unit' of turbulence in stratified plane-Couette flow.

Recently, and in ongoing work, we have been running and analyzing DNS of a stratified exchange flow which is a close representation of the stratified inclined duct (SID) experiment. By forcing the momentum and density equations, we are able to maintain several of the flow regimes observed in the SID experiments including nonlinear Holmboe waves and fully turbulent stratified shear flow. Our objectives include describing the transition between these regimes in terms of the flow parameters and characterising the mixing. This will provide additional insight into the SID experiments.

Objective 4
To synthesise the results of the mathematics, experiments and numerical simulations to determine the dependence of mixing rates and transport on the flow properties and relate them to the overall flow configurations.

Key findings
One of the important new findings from our experiments and numerical simulations is the strong sensitivity of stratified turbulence to the Peclet number. This overturns conventional wisdom which held that turbulent motions would be relatively unaffected by molecular diffusion. We found instead that stratified flows with large Peclet number can develop sharp and highly stratified interfaces either near horizontal boundaries [21] or in the interior of the flow [32]. In [21], we developed a new theory to predict the influence of the Peclet number on the flow properties of wall-bounded stratified turbulence. In [24] we developed a new theory to explain the formation and maintenance of density interfaces in the interior of stratified turbulent flow. This led to the identification of a new parameter formed by taking the product of the Prandtl number and the buoyancy Reynolds number. Numerical simulations [21, 24] suggest that this parameter controls the development of layers and the maintenance of interfaces in stratified turbulence.

At a simpler level, we demonstrated that the mixing found in both VRM experiments and 3D numerical simulations can be captured surprisingly well by a one-dimensional turbulence model tracking the evolution of the coherent kinetic energy found in the vortex ring, the generation of turbulence and available potential energy, and the ultimate division into dissipation and background potential energy [34].

Analysis of the energetics of the regime transitions in SID [41], the quantification of irreversible mixing with identifiable coherent structures [29] and numerical computations of mixing [21] provide clues concerning the rates of mixing and the dependence on the overall flow properties and the structures that are primarily responsible. There still remain many outstanding questions and to address these we are continuing the research with additional funding support. In particular, we are building a new SID experiment that allows for longer run times and different duct cross-sections. We are also continuing the DNS of exchange flows that are showing increasing similarity to the experiments. The challenge of high Prandtl number is still a significant issue. Finally, we are continuing to study the underlying mathematical structures that have been at the core of the MUST project.






References
1. Meyer, C. R. and Linden, P. F., (2014) Stratifed shear flow: experiments in an inclined duct, J. Fluid Mech., 753, 242-253
2. Kaminski, A. K. and Caulfield, C. P. and Taylor, J. R., (2014) Transient growth in strongly stratified shear layers, J. Fluid Mech., 758, R4
3. Manucharyan, G. E. and Caulfield, C. P., (2015) Entrainment and mixed layer dynamics of a surface-stress-driven stratified fluid, J. Fluid Mech., 765, 653-667
4. Lin, T. Y. and Caulfield, C. P. and Woods, A. W., (2015) Buoyancy-induced turbulent mixing in a narrow tilted tank, J. Fluid Mech., 773, 267-297
5. Deusebio, E and Caulfield, C. P. and Taylor, J. R., (2015) The intermittency boundary in stratified plane Couette flow, J. Fluid Mech., 781, 298-329
6. Olsthoorn, J. and Dalziel, S. B., (2015) Vortex-ring-induced stratified mixing, J. Fluid Mech., 781, 113-126
7. Zhou, Q. and Diamessis, P. J., (2015) Lagrangian flows within reflecting internal waves at a horizontal free-slip surface, Physics of Fluids, 27,126601
8. Eaves, T. S. and Caulfield, C. P., (2015) Disruption of SSP/VWI states by a stable stratification, Journal of Fluid Mechanics, 784, 548--564
9. Zhou, Q. and Diamessis, P. J., (2016) Surface manifestation of internal waves emitted by submerged localized stratified turbulence, J. Fluid Mech., 798, 505-539
10. Salehipour, H and Caulfield, C. P. and Peltier, W. R., (2016) Turbulent mixing due to the Holmboe wave instability at high Reynolds number, J. Fluid Mech., 803, 591-621
11. Leclercq, C. and Partridge, J. L. and Augier, P. and Dalziel, S. B. and Kerswell, R., (2016) Using stratification to mitigate end-effects in quasi-Keplerian Taylor-Couette flow, J. Fluid Mech., 791, 608-630.
12. Falder, M and White, N. J. and Caulfield, C. P., (2016) Seismic imaging of rapid onset of stratified turbulence in the south Atlantic Ocean, J. of Physical Oceanography, 46, 1023--1044
13. Portwood, G. D. and de Bruyn Kops, S. M. and Taylor, J. R. and Salehipour, H and Caulfield, C. P., (2016) Robust identification of dynamically distinct regions in stratified turbulence, J, of Fluid Mech., 807, R2
14. Burridge, H. C. and Partridge, J. L. and Linden, P. F., (2016) The fluxes and behaviour of plumes inferred from measurements of coherent structures within images of the bulk flow, Atmosphere-Ocean, 403-417
15. Taylor, J. R. and Deusebio, E and Caulfield, C. P. and Kerswell, R. R., (2016) A new method for isolating turbulent states in transitional stratified plane Couette flow, Journal of Fluid Mechanics, 808, R1
16. Hughes, G. O. and Linden, P. F., (2016) Mixing efficiency in run-down gravity currents, J. Fluid Mech., 809, 691-704
17. Rao, P. and Caulfield, C. P. and Gibbon, J. D., (2017) Nonlinear effects in buoyancy-driven variable-density turbulence, J. of Fluid Mech., 810, 362-377
18. Eaves, T. S. & Caulfield, C. P., (2017) Multiple instability of layered stratified plane Couette flow, J. Fluid Mech., 813, 250-278
19. Mashayek, A., Salehipour, H., Bouffard, D., Caulfield, C. P., Ferrari, R., Nikurashin, M., Peltier, W. R. & Smyth, W. D., (2017) Efficiency of turbulent mixing in the abyssal ocean circulation, Geophysical Research Letters, 44, 6296--6306
20. Olsthoorn, J. and Dalziel, S. B. (2017) Three-dimensional visualization of the interaction of a vortex ring with a stratified interface, J. Fluid Mech. 820, 549-579.
21. Zhou, Q and Taylor, J. R. and Caulfield, C. P., (2017) Self-similar mixing in stratified plane Couette flow for varying Prandtl number, J. Fluid Mech., 820, 86-120.
22. Burridge, H. C. and Parker, D. A. and Kruger, E. S. and Partridge, J. L. and Linden, P. F., (2017) Conditional sampling of a high Peclet number turbulent plume and the implications for entrainment, J. Fluid Mech., 823, 26-56
23. Zhou, Q and Taylor, J. R. and Caulfield, C. P. and Linden, P. F., (2017) Diapycnal mixing in layered stratified plane Couette flow quantified in a tracer-based coordinate, J. Fluid Mech., 823, 189-229
24. Taylor, J. R. and Zhou, Q, (2017) A multi-parameter criteria for layer formation in a stratified shear flow using buoyancy coordinates, J. Fluid Mech., 823, R5
25. Kaminski, A. K. and Caulfield, C. P. and Taylor, J. R., (2017) Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers, J. of Fluid Mech., 825, 213-244
26. Dickinson, A and White, N. J. and Caulfield, C. P., (2017) Spatial variation of diapycnal diffusivity estimated from seismic imaging of internal wave field, Gulf of Mexico, J. of Geophysical Research: Oceans, 122, 9827--9854
27. Gunn, K. L. and White, N. J. and Larter, R. D. and Caulfield, C. P., (2018) Calibrated Seismic Imaging of Eddy-Dominated Warm-Water Transport Across the Bellingshausen Sea, Southern Ocean, Journal of Geophysical Research: Oceans, 123, 3072--3099
28. Lucas, D. and Caulfield, C. P. and Kerswell, R. R., (2017) Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities, J. Fluid Mech., 832, 409--437
29. Lucas, D. and Caulfield, C. P., (2017) Irreversible mixing by unstable periodic orbits in stratified turbulence, J. Fluid Mech., 832, R1
30. Olsthoorn, J. & Dalziel, S.B., (2017) Vortex-ring-induced stratified mixing.J. Fluid Mech.., 832, 129-146.
31. Olsthoorn, J. & Dalziel, S.B., (2017) Three-dimensional visualization of the interaction of a vortex ring with a density interface. J. Fluid Mech., 820, 549-579.
32. Olvera, D. & Kerswell, R. R. (2017) Exact coherent structures in stably-stratified plane Couette flow. J. Fluid Mech., 826, 583-614
33. Olvera, D. & Kerswell, R. R. (2017) Optimising energy growth as a tool for finding exact coherent structures. Phys. Rev. Fuids., 2, 083902.
34. Olsthoorn, J. and Dalziel, S. B. (2018) Vortex-ring-induced stratified mixing: mixing model J.Fluid Mech. 837, 129-146
35. Taylor, J. R. and Caulfield, C. P., (2018) Testing marginal stability in stratified mixing: mixing model shear layers, J. Fluid Mech., 837, 129-146.839, R4
36. Lefauve, A. and Partridge, J. L. and Zhou, Q and Dalziel, S. B. and Caulfield, C. P. and Linden, P. F., (2018) The structure and origin of confined Holmboe waves,J. Fluid Mech, 848, 508--544
37. Marcotte, F. and Caulfield C. P. (2018) Optimal mixing in two-dimensional stratified plane Poiseuille flow at finite Peclet and Richardson numbers, J. Fluid Mech., 853, 359-385.
38. Salehipour, H. and Peltier, W. R. and Caulfield, C. P. (2018) Self-organized criticality of turbulence in strongly stratified mixing layers, J. Fluid Mech, 856, 228--256
39. Sutherland, B. R. and Achatz, U and Caulfield, C. P. and Klymak, J. M., (2019) Recent progress in modeling imbalance in the atmosphere and ocean, Phys. Rev. Fluids, 4, 010501
40. Partridge, J. L., Lefauve, A. and Dalziel, S. B., (2019) A versatile scanning method for volumetric measurements of velocity and density fields. Measurement Science and Technology. In press
41. Lefauve, A., Partridge, J. L. & Linden, P. F. (2019) Regime transitions and energetics of sustained stratified shear flows. J. Fluid Mech. In review
42. Lucas, D., Caulfield, C.P. and Kerswell, R.R. (2019) Layer formation and relaminarisation in plane Couette flow with spanwise stratification J. Fluid Mech. In press.
43. Page, J & Kerswell, R. R. (2019) Koopman analysis of Burgers equatioin. Phys. Rev. Fluids, 3, 07190(R)
44. Page, J & Kerswell, R. R. (2019) Koopman mode expansions between simple invariant solutions. PRF Under review
45. van Reeuwijk, M. and Holzner, M. and Caulfield, C. P (2019). Mixing and entrainment are suppressed in inclined gravity currents, (under review at J. Fluid Mech.)
46. Portwood, G. D. and de Bruyn Kops, S. M. and Caulfield, C. P. (2019) Asymptotic dynamics of high dynamic range stratified turbulence (under review at PRL)
47. Gunn, K. L. and Caulfield, C. P. and White, N. J. Time-Lapse Seismic Imaging of Oceanic Fronts and Large-Scale Stirring in South Atlantic Ocean (2019) (under review at GRL)
48. Taylor, J. R. and de Bruyn Kops, S. M. and Caulfield, C. P. and Linden, P. F. (2019) Testing the assumptions underlying ocean mixing methodologies using direct numerical simulations, (under review at Journal of Physical Oceanography)
49. Langham, J., Eaves, T. & Kerswell, R.R. (2019) Effect of Prandtl number on stably stratified exact coherent structures. In preparation.
Exploitation Route We hosted Euromech 567 in March 2015 and will host a Royal Society meeting to be held in March 2016 to discuss the findings and interact with the wider community. Euromech 567 was attended by over 70 participants.
Sectors Aerospace, Defence and Marine,Chemicals,Education,Energy,Environment,Manufacturing, including Industrial Biotechology

URL http://damtp.cam.ac.uk/research/env/must/
 
Description EPSRC Impact Acceleration Award
Amount £50,000 (GBP)
Funding ID LEAG/553 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 02/2016 
End 02/2017
 
Title 3D PIV & PLIF 
Description The development of new capability to measure the three velocity components and the density field over a volume in stratified fluid flow 
Type Of Material Improvements to research infrastructure 
Year Produced 2018 
Provided To Others? Yes  
Impact None as yet 
 
Title 3C3Ds PIV/LIF 
Description Development of novel technique for obtaining near-instantaneous measurements of velocity (3 components) and density/concentration across a three-dimensional domain 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact Providing a unique method of extracting high-resolution, time-resolved measurements from fluid flows. Has already lead to new discoveries. 
 
Title Data supporting 'Testing linear marginal stability in stratified shear layers' 
Description The Diablo input files required to re-run the simulations outlined in the journal article, and the numerical data required to recreate figures 1, 3 and 4 in the paper. 
Type Of Material Database/Collection of data 
Year Produced 2018 
Provided To Others? Yes  
 
Title Dataset supporting "Role of overturns in optimal mixing in stratified mixing layers" 
Description Matlab figure files used to create key figures 2-7 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title Datasets supporting "Optimal mixing in three-dimensional plane Poiseuille flow at high Péclet number" 
Description Data sets used to generate simulations and figures for JFM paper entitled "Optimal mixing in three-dimensional plane Poiseuille flow at high Péclet number" by L. Vermach and C. P. Caulfield 
Type Of Material Database/Collection of data 
Year Produced 2018 
Provided To Others? Yes  
 
Title Initial conditions for minimal seeds 
Description Initial conditions for minimal seeds reported in Eaves & Caulfield (2015): J. Fluid Mech. 784 10.1017/jfm.2015.596 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact none as yet 
URL https://www.repository.cam.ac.uk/handle/1810/251121
 
Title Koopman modes for laboratory experiments 
Description Development of algorithms for Dynamic Mode Decomposition (DMD) relevant to experimental observations of turbulent flows in stratified fluids. 
Type Of Material Data analysis technique 
Year Produced 2015 
Provided To Others? Yes  
Impact Insight into the time-varying modal structure of nonlinear flows. 
 
Title Research data supporting "Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence" 
Description Data set used to construct key figures. 
Type Of Material Database/Collection of data 
Year Produced 2018 
Provided To Others? Yes  
 
Title Research data supporting "Koopman analysis of Burgers equation" 
Description The supporting data includes (1) 2 solutions of the Burgers equation (in the folder bur_traj) obtained on a domain of length L=6pi with viscosity parameter nu=0.1 and evaluated at N=250 Gauss-Lobatto points. The snapshots are stored every 0.1 advective time units for a total evolution time of T=60. Files with the prefix 'bur_00.' are for the initial condition u(x) = exp( -(x+pi/2)^2 ); those with prefix 'bur_02.' are for the initial condition u(x) = sin(2 pi x / L). (2) Accompanying python code to perform dynamic mode decomposition (DMD) of this data. The file burgers_example.py is essentially a step by step guide for performing DMD on this dataset using different observable functions. 
Type Of Material Database/Collection of data 
Year Produced 2018 
Provided To Others? Yes  
 
Title Research data supporting "Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities". 
Description Initialisation data for the various simulations and figure data in gnuplot and vapor form. Research supported by the MUST programme grant. 
Type Of Material Database/Collection of data 
Year Produced 2018 
Provided To Others? Yes  
 
Title Research data supporting Three-Dimensional Visualization of the Interaction of a Vortex Ring with a Stratified Interface 
Description Data associates with the paper "Three-Dimensional Visualization of the Interaction of a Vortex Ring with a Stratified Interface," which has been accepted for publication in the Journal of Fluid Mechanics. The work investigates the velocity field evolution of a vortex ring impacting a stratified interface. The 3D velocity field data is stored in a NetCDF3 file format. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title Research data supporting Vortex-ring-induced stratified mixing: mixing model 
Description Data associated with the publication "Vortex-ring-induced stratified mixing: mixing model." Includes model implementation and mixing data. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title SID experiments 
Description Experimental data describing the flow in a Stratified Inclined Duct. 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact Publication of journal article. Input into other components of research. 
 
Title STC experiments 
Description Experimental measurements of Stratified Taylor-Couette flow 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact Publication of journal article. Input into other components of research. 
 
Title Supporting data for Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers 
Description This directory contains the source code and input files for all direct numerical simulations and calculations of the linear optimal perturbations reported in the accompanying paper. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title Supporting data for Self-similar mixing in stratified plane Couette flow for varying Prandtl number 
Description The directory contains the Fortran source code, initial conditions, input and grid files used to produce the direct numerical simulations reported in "Self-similar mixing in stratified plane Couette flow for varying Prandtl number" 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title Supporting data for: A multi-parameter criterion for layer formation in a stratified shear flow using sorted buoyancy coordinates 
Description This contains supporting data needed to reproduce the DNS simulations reported in the accompanying paper. The files include source code (in Fortran 90/MPI) and input files. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title Supporting data for: Diapycnal mixing in layered stratified plane Couette flow quantified in a tracer-based coordinate 
Description This dataset contains the source code, input files, and grid files needed to re-produce the DNS simulations reported in the linked paper. Initial conditions are also included in the HDF5 file format. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title Supporting data for: Testing the assumptions underlying ocean mixing methodologies using direct numerical simulations 
Description This dataset contains output from direct numerical simulations. The directory contains a README file which explains how to load the data and a description of the variables 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Title Supporting dataset for "Efficiency of turbulent mixing in the abyssal ocean circulation" by Mashayek et al in Geophysical Research Letters 
Description Data used to construct figures in publication. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
 
Title 3D Experimental diagnostics 
Description Software algorithms for controlling experiments and analysing image sequences to obtain near-instantaneous time- and space-resolved three-dimensional measurements across an extended three-dimensional volume. 
Type Of Technology Software 
Year Produced 2016 
Impact The first approach to provide near-instantaneous measurement of density and three components of velocity spanning an extended three-dimensional volume. 
 
Title 64-bit Experimental diagnostics 
Description Software algorithms for controlling experiments and analysing image sequences including obtaining near-instantaneous time- and space-resolved three-dimensional measurements across an extended three-dimensional volume. The software has been migrated from 32-bits to 64-bits. The software is proprietary (rather than Open Source), but licences are freely available. 
Type Of Technology Software 
Year Produced 2018 
Impact The first approach to provide near-instantaneous measurement of density and three components of velocity spanning an extended three-dimensional volume. 
 
Title Koopman modes for laboratory experiments 
Description Development of algorithms for Dynamic Mode Decomposition (DMD) to extract Koopman modes relevant to experimental observations of turbulent flows in stratified fluids. 
Type Of Technology Software 
Year Produced 2015 
Impact Insight into the time-varying modal structure of both linear and nonlinear flows. Has been applied across a broad range of flows in the laboratory. 
 
Description A talk at 70th APS DFD Denver 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Research presentation at international conference
Year(s) Of Engagement Activity 2017
 
Description APS (Boston, 2015) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Contributed talk: Turbulent mixing by buoyancy-driven flows in long tubes
Year(s) Of Engagement Activity 2015
 
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 Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk at Scotland-Norway meeting on Internal Waves
Year(s) Of Engagement Activity 2017
 
Description EUROMECH (Cambridge) 2015 
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: On the meaning of mixing efficiency when there is available potential energy
Year(s) Of Engagement Activity 2015
 
Description Engineering Science (Auckland) 
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: Water bombs and other fun things
Year(s) Of Engagement Activity 2016
 
Description Euromech 567 Colloquium - AKK 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Alexis Kaminski presented work at the Euromech Colloquium held in Cambridge, UK in collaboration with Colm-Cille Caulfield and John Taylor
Year(s) Of Engagement Activity 2015
 
Description Euromech 567 Colloquium - ED 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Enrico Deusebio presented results from simulations of Stratified Plane Couette flow from the MUST project to the Euromech Colloquium in Cambridge, UK in March 2015.
Year(s) Of Engagement Activity 2015
 
Description Euromech 567 Colloquium - JRT 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact John Taylor presented results from the MUST project at the Euromech Colloquium in March 2015
Year(s) Of Engagement Activity 2015
 
Description FDSE Summer School; even years from 2012 
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 The Biennial Summer School on the Fluid Dynamics of Sustainability and the Environment attracts ~50 students from across the world. The School is aimed at postgraduate students and postdocs, and brings in leading academics from around the world. The School extends over two weeks with participants engaging in a combination of lectures, laboratory experiments and numerical simulations.
Year(s) Of Engagement Activity 2012,2014,2016
URL http://www.fdse.org
 
Description Fluid Dynamics seminar in the Department of Mechanical and Aerospace Engineering, University of California, San Diego. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Presented new results from MUST to faculty and students at UCSD.
Year(s) Of Engagement Activity 2016
 
Description GKB lecture 
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 I gave the plenary lecture at the 20th Australasian Fluid Mechanics Conference in Perth, Australia.
Year(s) Of Engagement Activity 2017
URL http://www.afms.org.au/20AFMC/speakers.html
 
Description IMA Conference on Waves & Turbulence (Julian Hunt's Birthday) 
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: 9. Rayleigh-Taylor mixing: is it robust to the dynamics?
Year(s) Of Engagement Activity 2016
 
Description IWPCTM15 
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: Attempts to escape initial conditions
Year(s) Of Engagement Activity 2016
 
Description Internal waves conference Edinburgh 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The talk was part of a joint meeting held between the Norwegian Academy of Science and the Royal Society of Scotland. It sparked questions and there may be future collaborations
Year(s) Of Engagement Activity 2015
URL https://sites.dev.dundee.ac.uk/norway-scotland-waves/2015/07/4th-norway-scotland-waves-symposium/
 
Description Invited participation at extended programme in Santa Barbara 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Invited participation at extended programme on "Clockwork of turbulence" at Kavli Institute of Theoretical Physics, UC Santa Barbara, changing philosophy of study of turbulence from statistics to structures.
Year(s) Of Engagement Activity 2017
URL http://online.kitp.ucsb.edu/online/transturb17/caulfield2/
 
Description Invited talk at the American Physical Society Division of Fluid Dynamics meeting in Boston, USA 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Alexis Kaminksi presented her work at the APS DFD meeting joint with Colm-Cille Caulfield and John Taylor in an oral presentation.
Year(s) Of Engagement Activity 2015
 
Description Invited talk at the American Physical Society Division of Fluid Dynamics meeting in Boston, USA 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact John Taylor presented results from the MUST project
Year(s) Of Engagement Activity 2015
 
Description Invited talk in Paris 
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 at meeting co-organised by CEA and AWE. Meeting in Paris, April 2017: "Workshop meeting on turbulent mixing and ejecta at interfaces". Participants from CEA, AWE and academia.
Year(s) Of Engagement Activity 2017
 
Description Lectured and organized computational projects at the Fluid Dynamics for Sustainability and the Environment summer school in Cambridge, UK 
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 About 40 PhD students attended the two week long summer school and learned basic principles about Fluid Dynamics applied to the natural and built environment. After the summer school the students reported that they gained significantly from the experience. This experience should have a significant impact on the research conducted during their PhD and beyond.
Year(s) Of Engagement Activity 2016
 
Description Leverhulme meeting Oxford 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The talk was part of a Leverhulme funded network, aimed at generating collaborative projects. It sparked questions and there may be future collaborations
Year(s) Of Engagement Activity 2015
 
Description Leverhulme network meeting on waves and turbulence 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact A workshop at the University of Cambridge organized by Peter Davidson with invited participants including leading scientists from around the world.
Year(s) Of Engagement Activity 2016
 
Description Linne Centre Annual Lecture January 2018 Stockholm 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Annual Lecture at Linne Flow Centre, KTH Stockholm Retreat.
Year(s) Of Engagement Activity 2018
 
Description Open Day 2017 
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 2017, there were around 700 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 2017
 
Description PFL@70 - invited talk, March 2017 
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 at 70th birthday meeting for Prof. P.F. Linden
Year(s) Of Engagement Activity 2017
 
Description Participation in extended workshop in Los Angeles 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Key participant in extended programme on the Mathematics of Turbulence: invited talk in specific workshop on the Mathematics of Mixing
Year(s) Of Engagement Activity 2014
 
Description Participation in workshop at Fields Institute, Toronto 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact Workshop on extreme events and criticality in turbulence, leading to extended collaborations on stratified mixing.
Year(s) Of Engagement Activity 2016
 
Description Plenary lecture at conference in San Diego 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Plenary lecture at 8th International Symposium in Stratified Flows in San Diego.
Year(s) Of Engagement Activity 2016
 
Description Presentation at European Turbulence Conference by John Taylor 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact John Taylor gave a presentation titled "Controlled direct numerical simulations of turbulent spots in a stratified shear flow" at the European Turbulence Conference in August, 2017
Year(s) Of Engagement Activity 2017
 
Description Presentation at the 2017 meeting of the American Physical Society 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Gave an oral presentation at the annual American Physical Society meeting, division of fluid dynamics.
Year(s) Of Engagement Activity 2016
 
Description Presentation to Trinity Mathematics Society 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Undergraduate students
Results and Impact Outreach talk to undergraduate students March 2018
Year(s) Of Engagement Activity 2018
 
Description Public Open Day 2015 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Public/other audiences
Results and Impact An interactive laboratory experiment motivated by work related to this grant formed a centrepiece for a Public Open Day in the GK Batchelor Laboratory (DAMTP). This even attracted around 700 people to the laboratory.
Year(s) Of Engagement Activity 2015
 
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 Research visit Chinese University of Hong Kong April 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Talk and research visit to CUHK.
Year(s) Of Engagement Activity 2017
 
Description 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 Pedagogical lectures at an international summer school in France
Year(s) Of Engagement Activity 2015
URL http://fdse.org
 
Description Summer school Undine Italy 
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 Pedagogical lectures based on the research in this grant
Year(s) Of Engagement Activity 2015
 
Description Talk at Department of Ocean Engineering Shanghai Jiao Tong April 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Presentation at Shanghai Jiao Tong to students
Year(s) Of Engagement Activity 2017
 
Description Talk at European Turbulence Conference Stockholm 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Presentation at European Turbulence Conference in Stockholm
Year(s) Of Engagement Activity 2017
 
Description Talk at NYU Shanghai March 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Undergraduate students
Results and Impact Presentation to students at NYU Shanghai
Year(s) Of Engagement Activity 2017
 
Description Talk at Ocean Sciences Meeting Portland February 2018 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Research Talk at Ocean Sciences Meeting Portland
Year(s) Of Engagement Activity 2018
 
Description Talk at South China Sea Institute of Oceanology April 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Research presentation to Chinese oceanographers
Year(s) Of Engagement Activity 2017
 
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
 
Description Workshop at Banff International Research Station 
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 Co-organised workshop on imbalance in the atmosphere/ocean
Year(s) Of Engagement Activity 2018