Physics of Turbulence

Turbulent flows are characterized by an intricate energy cascade which redistributes energy from large scales, where it is injected, to small scales, where it is eventually dissipated into heat. This cascade and dissipation process endow the small scales with certain universal properties, thus making them particularly important for understanding the physics of turbulence and for developing accurate predictive models. 

Our group is at the forefront of in this field, utilizing world's fastest supercomputers to perform some of the biggest turbulence simulations. By combining them with rigorous theoretical frameworks, we are able to significantly advance our understanding of the fundamental physics of turbulence. This also sets the stage for developing transformative turbulence models of to address complex challenges across various science and engineering disciplines. 

Deep learning meets turbulence

In most practical applications, the vast range of scales in turbulence prohibits a high-fidelity direct simulation. Instead, one must resolve a limited range of scales, while modeling the rest. Traditionally, this modeling has been performed through "human learning", where scientists and engineers develop simplified, interpretable models that, while useful, are limited in accuracy and generalizability.

Our research group is working on overcoming these limitations by harnessing deep machine learning to develop large models that substantially enhance accuracy compared to traditional approaches. In particular, by learning small scale dynamics from an extensive database of fully resolved simulations at lower turbulence intensities, our models not only deliver improved accuracy for under-resolved simulations at much higher turbulence intensities, but also have the capability to generalize effectively across different flow conditions. 

Turbulent mixing and transport

From mixing cream into coffee to fuel and oxidizer in car or aerospace engines, and from distribution of heat, salt and biomatter in oceans to spread of pollutants or water vapor in the atmosphere, turbulence plays an indispensable role in shaping life as we know it. However, various transport processes fundamentally differ in their physics depending on various controlling parameters, making turbulent mixing even more complex and challenging to study than just turbulence itself.  

Expanding our research on small scale turbulence, our group focuses on uncovering universal properties of turbulent mixing and particle dispersion, with particular relevance for geophysical and environmental applications. We leverage massive numerical simulations to gain physical insights into the fundamental mechanisms driving turbulent transport and complement it deep learning methods to develop transformative models for applications.

Vortex dynamics 

Vortices are the fundamental building blocks of all fluid flows. They range from persistent large-scale global circulation patterns that govern weather systems, to wing-tip vortices behind airplanes that induce additional drag, to short-lived microscopic whorls that dictate how heat, chemicals and particles are mixed and transported in a flow. The dynamics and interactions of vortices are thus at the core of fluid dynamics and turbulence.

Our group is pioneering new insights into vortex dynamics by integrating novel theoretical approaches with cutting-edge simulations. We particularly focus on microscopic vortices that arise spontaneously in all turbulent flows, aiming not only to advance turbulence theory and modeling, but also provide critical physical insights into the regularity of the Navier-Stokes equations—a profound and long-standing question in mathematical physics that remains one of the unsolved Clay Millennium Prize problems.