I am interested in developing models and simulation methods for turbulent flows. Turbulent flows are characterised by chaotic or random eddies. They are ubiquitous in the nature and industrial applications (the movement of the atmosphere, the waves in the ocean etc). Mathematically they are described by high dimensional chaotic nonlinear dynamical systems with a large number of variables, these variables describing the motion of "eddies" of very different sizes. Turbulent motion enhances mixing and heat exchange but its chaotic nature severely limits our ability, e.g., to make accurate weather prediction, or to plan pollution control, or to understand the formation of stars. It is a topic of tremendous importance.

As there are no general closed form solutions to the problem, my research relies heavily on numerical simulations. The main themes of my research are summarized below. The full publication list can be found on my google scholar page . I am always looking for motivated PhD candidates. There are opportunities for PhD projects in each of these themes. If you find them interesting, feel free to drop me an email or apply through the university application portal .

## Downscaling

For multi-scale systems such a turbulent flow, the challenge very often is 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.

## Flow optimisation with data assimilation

Data assimilation refers to a suite of methods by which we synthesize 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 - yes, 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 spreading and mixing things up, which underpins many physical processes (e.g. 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. This is another topic that I have taken interests in.