The scientific discipline of fluid dynamics is primarily concerned with the measurement, modelling and underlying physics and mathematics of how liquids and gases behave. Almost all natural and manufactured systems involve the flow of fluids, which are often complex. Consequently, an understanding of fluid dynamics is integral to addressing major societal challenges including industrial competitiveness, environmental resilience, the transition to net-zero and improvements to health and healthcare. Fluid dynamics is essential to the transition of the energy sector to a low-carbon future (for example, fluid dynamics simulations coupled with control algorithms can significantly increase wind farm efficiency). It is vital to our understanding and mitigation of climate change, including extreme weather events (for example in designing flood mitigation schemes). It is key to the digitisation of manufacturing through 3d printing/additive manufacturing and development of new greener processing technologies. In healthcare, computational fluid dynamics in combination with MRI scanning provides individualised modelling of the cardio-vascular system enabling implants such as stents to be designed and tested on computers. Fluid dynamics also shows how to design urban environments and ventilate buildings to prevent the build-up of pollutants and the transmission of pathogens. The UK has long been a world-leader in fluid dynamics research. However, the field is now advancing rapidly in response to the demand to address more complex and interwoven problems on ever-faster timescales. Data-driven fluid dynamics is a major area where there are rapid advances, with the increasing application of data-science and machine learning techniques to fluid flow data, as well as the use of Artificial Intelligence to accelerate computational simulations. For the UK to maintain its competitive position requires an investment in training the next generation of research leaders who have experience of developing and applying these new techniques and approaches to fluids problems, along with professional and problem-solving skills to lead the successful adoption of these approaches in industry and research. The University of Leeds is distinctive through the breadth, depth and unified structure of its fluid dynamics research, coordinated through the Leeds Institute for Fluid Dynamics (LIFD), making it an ideal host for this CDT. The CDT in Future Fluid Dynamics (FFD-CDT) will build on the experience of successfully running a CDT in Fluid Dynamics to address these new and exciting needs. Our students will carry out cutting-edge research developing new fluid dynamics approaches and applying them across a diverse range of engineering, physics, computing, environmental and physiological challenges. We will recruit and train cohorts of students with diverse backgrounds, covering engineering, mathematical, physical and environmental sciences, in both the fundamental principles of fluid dynamics and new data-driven methodologies. Alongside this technical training we will provide a team-based, problem-led programme of professional skills training co-developed with industry to equip our graduates with the leadership, team-working and entrepreneurial skills that they need to succeed in their future careers. We will build an inclusive, diverse and welcoming community that supports cross-disciplinary science and effective and productive collaborations and partnerships. Our CDT cohort will be at the heart of growing this capability, integrated with and within the Leeds Institute for Fluid Dynamics to deliver a dynamic and vibrant training and research environment with strong UK and international partnerships in academia, industry, policy and outreach.

A new mathematical theory for stochastic flows composed of active particles making discrete decisions will open new avenues of research and build towards novel solutions to challenges in traffic and pedestrian management. Active matter systems are composed of large numbers of individual elements that consume energy to move and interact. From flocking birds to driven colloids, many interesting phenomena in this field cannot be understood within the historically successful theories of fluid dynamics and equilibrium thermodynamics, making this an exciting and challenging field. In the vast majority of active matter models particles respond smoothly to their environments. A step-change in both real-world applicability and mathematical depth will be achieved by considering particles that move continuously but make discrete changes of state. In applications these state changes might represent agents making decisions or abruptly adjusting behaviour in response to others. To motivate the programme and maintain focus, we will develop our framework with reference to two key applications: traffic and pedestrian flows. Subject to both continuous random fluctuations and discrete demographic noise arising from the random timing of state changes, these active flows have a rich set of behaviours. The research programme proposed here will open a new field of study between traditional applied mathematics and probability, with methods applicable to mathematical research spanning evolutionary biology to robotics.

To counter significant levels of climate change and biodiversity loss, the UK and numerous other countries have set targets for "net-zero" greenhouse gas emissions. Rapid reductions in the built environment are crucial, since it drives 42% of global energy-related carbon dioxide emissions. To achieve net-zero carbon buildings, we must reduce both: 1. OPERATIONAL CARBON - the emissions caused by a building's operational use 2. EMBODIED CARBON - the emissions caused by 'everything else', such as the manufacturing of materials, transportation to site, onsite construction, refurbishment, and disposal. Given the huge amount of construction required for new build and retrofit around the world, it is critical that embodied carbon is addressed, while we continue to tackle operational carbon. Indeed, the UK Government's 'Industrial Strategy: Construction Sector Deal' aims to halve the greenhouse gas emissions from the built environment by 2025, and to shift focus from operational to whole-life performance. Since May 2019, over 1,000 architecture and engineering practices have committed to reducing both embodied and operational carbon (these are together referred to as whole-life carbon; WLC). The Royal Institute of British Architects has set WLC targets for 2030 and 2050 in its 'Climate Challenge', and the new London Plan will require all 'referable planning applications' to calculate and reduce WLC. However, there are persistent challenges to predicting embodied (and therefore whole-life) carbon, and thus minimising it in practice. In particular, uncertainty is typically ignored. At the levels of individual construction products and whole buildings, models are typically deterministic in nature, producing single-point estimates of WLC. In practice, it is then unclear how confident designers and engineers can be that one option will be lower-carbon than another. In other scientific disciplines, probabilistic approaches are more common, producing results with confidence intervals and using statistical significance tests when making comparisons. Such rigour is now essential for predicting the WLC of buildings, to ensure that low-carbon design intentions are achieved in reality. This research therefore aims to significantly improve the treatment of uncertainty when predicting the WLC of construction products and whole buildings. We will work with project partners across the supply-chain of low-carbon buildings, including product manufacturing, low-carbon policy, and the design of structures and buildings. At product level, we will improve the treatment and communication of uncertainty in Environmental Product Declarations. At building level, we will develop and test a probabilistic approach for predicting whole life carbon through the design process. To achieve impact, we will engage international initiatives and standards that will define industry practice into the future.

The UK has one of the oldest building stocks in Europe. In England, around a quarter of this stock is of solid brickwork construction. Every year, thousands of such buildings experience structural distress due to seasonal and excavation-induced ground movements. To understand and manage the impact of ground movements on these historic assets, an in-depth knowledge of their materials is necessary. Standard techniques for characterising the mechanical properties of brick masonry materials require extensive sampling and destructive testing. As a result, these techniques are rarely applied to existing buildings. In-situ testing and characterisation of materials is a promising alternative. However, in their current form, standard in-situ tests provide limited information on material properties. The MINT project aims to develop a minor-destructive in-situ testing method to identify the key macro-scale deformability and strength parameters of historic brick masonry materials. This method will combine unconventional flat jack testing with unambiguous Digital Image Correlation strain measurements and rapid Virtual Fields Method algorithms to overcome the limitations of standard material characterisation techniques. It will deliver a step change in our ability to collect detailed mechanical information on brick masonry materials and unlock the potential of numerical simulations to reliably assess structural response. It is envisioned that this new capability will also enable more informed decisions on retrofit and repair. In the longer term, the developments from MINT will contribute to improve productivity in the construction sector, and the welfare of the general public.