Dr Yi Li

School of Mathematical and Physical Sciences


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+44 114 222 3882

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Dr Yi Li
School of Mathematical and Physical Sciences (nee maths)
Hicks Building
Hounsfield Road
S3 7RH
Research interests

Dr Yi Li's main research interests are in the field of fluid mechanics, in particular turbulence. Topics include fluid flow optimisation, simulation and modelling, and the application of signal processing and database techniques in the study of data-intensive fluid mechanics problems.

Turbulent flows are characterised by chaotic or random eddies. They are ubiquitous in nature and industrial applications (for example the movement of the atmosphere, the waves in the ocean). Mathematically they are described by high dimensional chaotic nonlinear dynamical systems with a large number of variables. These variables describe the motion of eddies of very different sizes. Turbulent motion enhances mixing and heat exchange but its chaotic nature severely limits our ability, for example to make accurate weather prediction, or to plan pollution control, or to understand the formation of stars. It is a topic of tremendous importance. We rely heavily on numerical simulations as there are no general closed form solutions to the problem.

Research themes

Dr Yi Li’s research themes are shown below.


For multi-scale systems such a turbulent flow, the challenge very often is that it is too time-consuming to simulate all scales. A practical approach is to simulate only the large scales, which capture the main features of the flows, whereas the small scales are replaced by simpler models. This practice is called downscaling or subgrid-scale modelling. One fruitful idea in this line of research is to leverage the observation that turbulent flows are self-similar, very much like fractals. We have developed new downscaling approaches which exploit the self-similarity property in novel ways.

More about fractals on the Fractal Foundation website

Flow optimisation with data assimilation

Data assimilation refers to a suite of methods by which we synthesise model-based numerical simulations with available experimental or observational data to improve model predictions. The idea shares some similarities with the Bayesian approach in statistical modelling. A difference is perhaps the models here are derived from fundamental physical principles such as momentum and energy conservation; as such are mostly deterministic or strongly constrained.

Data assimilation has attracted more attention recently given increased data availability and computational capacity. We have been using the approach to optimise subgrid-scale models. How to combine the self-similarity properties of turbulent flows with the approach is a key question. We are also looking into how machine learning can be combined with data assimilation to enhance the predictive capability of the models.

Because turbulent flows are chaotic, turbulence simulation with data assimilation is also closely related to a fascinating subject called chaos synchronisation. Even though chaotic trajectories are unpredictable, it is possible to synchronise them so that two trajectories oscillate unpredictably, but in exactly the same way. We have looked into turbulence simulations through this lens. There are many interesting questions to be answered!

Stochastic modelling

A main feature of turbulent flows is the enhanced ability to spread and mix things up, which underpins many physical processes (for example cloud formation, dispersion of plastic particles in the oceans). To understand this aspect of turbulent flows, an approach is to investigate the stochastic motion of small particles or bubbles in a turbulent flow field. This approach is called stochastic modelling.

PhD Projects

There are opportunities for PhD projects in each of these themes. If you find them interesting, you can contact Dr Yi Li by email YiLi@shef.ac.uk or apply through the university PhD application portal.


Journal articles

Conference proceedings papers

Working papers

Research group

Fluid Dynamics

Teaching activities
MAS322 Operations Research
MAS423 Advanced Operations Research
MAS422 Magnetohydrodynamics
MAS411 Topics in Advanced Fluid Mechanics