Research Area: Applied Mathematics, Fluids & Turbulence
Applied Mathematics, Turbulent fluid flow, wavelet methods My research focuses on the theory and computation of fluid turbulence, with a special interest in dynamically adaptive numerical methods based on the wavelet transform. There are numerous problems that remain unresolved in the theory of turbulence, despite more than 100 years of research on the subject. A complete and precise theory of turbulence would be useful in areas as diverse as aerodynamics, combustion, urban pollution modelling, weather prediction and climate modelling. Although we are still far from being able to formulate such a theory, much progress has been made in the last few decades. The aim of my research is to combine several recent discoveries in order to develop a new approach to turbulence modelling. These discoveries include wavelet transforms (which are used to compress data and solve partial differential equations), penalisation methods (which can be used with any numerical method to simulate complex geometries, such as an airplane), and coherent vortices (flow structures that control turbulence dynamics). Current research projects include adaptive multiscale climate modelling, fluid-structure interaction, compressive sampling and the role of turbulence in star formation.
Applied mathematics, turbulent fluid flow, wavelet methods