Developing mathematical models to incorporate microstructural heterogeneities into viscous flow

Ice and rocks flow viscously as complex non-Newtonian fluids. Current models commonly neglect several key rheological effects introduced by the heterogeneity of the materials' (micro)structure. The incorporation of these complex features into viscous fluid dynamics presents exciting research opportunities, to be addressed in this PhD project. An example concerns our ability to predict the rate of collapse of the Earth's ice sheets, which depends centrally on the dependence of ice rheology on the heterogeneities of its microstructure. Another is the movement of tectonic plates, which controls the occurrence and severity of earthquakes. Simulations in solid-Earth viscous flows typically apply isotropic models that are insufficient to describe leading-order characteristics of ice and rock flow dynamics because of the presence of microstructural heterogeneities: complexities at a small scale due to the presentence of differing material types (e.g. layering) and polycrystal arrangement (crystal grains, each oriented/slipping in different directions). This project presents an opportunity to address key open questions needed to close this gap in fluid-mechanical modelling of environmental systems. The effects of polycrystalline arrangement involves coupling a statistical representation of the material's microstructure with viscous anisotropy. The evolution of layers involves the analysis of the folding and necking instabilities associated with elastic and viscous beams separated by interstitial fluid of different material properties. The project thus presents a variety of directions, and the specific focus will be primarily mathematical, but otherwise tailored to the interests of the student.

The CDT will address the continued need of the UK for highly trained graduates in Fluid Dynamics and deliver impact through the novel research conducted by CDT students. The impact and benefits will reach multiple stakeholders.

Impacts on Skills and People:

Key beneficiaries of the CDT will be the alumni of our current and future programme and the organisations who employ them. Through the technical and professional development training, and the CDT environment, our graduates will have expertise in fundamental theory, analytical and numerical approaches, experimental techniques and application, and in-depth technical knowledge in their PhD area. Moreover they will have leadership, communication, responsible innovation and team working skills, combined with experience of working with academic and industry partners in a diverse and cross-disciplinary environment. This breadth and depth sets our CDT graduates apart from their peers, and positions them to become future leaders in industry, society and academia across a range of sectors. They will obtain the underpinning skills, and long term support through our Alumni Association, to drive future innovation across multiple sectors and act as life-long ambassadors for Fluid Dynamics.

The impact on people and skills will also include staff in our partner organisations in industry and non-profit sectors. Through participation in CDT activities, benefits will include new professional contacts and collaborations and knowledge of cutting edge methods and techniques. Through the CDT and the wider activities of Leeds Institute for Fluid Dynamics (LIFD) we will enhance the skills base in Fluid Dynamics and be the "go to" place to support high level training in end-user organisations.

Impact on Industry and the Economy:

In addition to the availability of trained graduates with excellent technical, professional and personal skills, impacts will arise from the direct innovation in research projects within the CDT. Research outcomes will influence processes, technologies, tools, guidelines and methodologies for our industry partners and other related organisations, leading to economic benefits such as new products, services and spin out companies. For example our current CDT has already led to 2 new patents (BAE Systems), student delivery of consultancy (Akzo Nobel), a flood demonstrator unit (JBA Trust) and a new method for hydraulic analysis (Hydrotec). Partners will also gain an enhanced reputation through being involved in successful and novel project outcomes. Skilled graduates and technology enhancement are key to economic growth, and our CDT will contribute to challenge areas such as energy, transport, the environment, the health sector, as well as those with chronic skills shortage such as the nuclear industry. Many of our partners are non-profit organisations, particularly in the environment and health sectors (e.g. NHS, PHE, Met Office). Impacts here derive through skilled graduates with the training and awareness to apply their expertise in organisations that deal with complex problems of societal importance, and novel research at the interface of disciplines. The cross-disciplinary nature of the CDT particularly supports this.

Impact on Society:

Beyond those who partner directly, many of the research projects have potential to lead to innovations with direct societal benefits (e.g. new techniques for detecting or controlling disease, new innovations in controlling flood risk or pollution, new insights into forecasting extreme weather). Beneficiaries here include professional bodies and government agencies who set policy, define guidance or influence the direction of innovation and research in the UK. The benefits to society will also stem from enhanced public awareness of Fluid Dynamics, both benefiting general public knowledge of science and inspiring the next generation (from all sectors of society) to undertake STEM careers.