Most fluid flows we encounter in nature and in technological applications are turbulent. Fluid turbulence occurs because the destabilizing inertial effect overwhelms the smoothing viscous effect (the ratio of the strength of the two mechanisms is measured by the Reynolds number). To date, despite very impressive progresses in the modeling and controlling of engineering flows, our understanding of the physics of turbulence is still limited. In fact, fluid turbulence is often called "the last unsolved problem in classic physics". Traditionally, studies of turbulence have been almost exclusively in the Eulerian frame, i.e., in a coordinate system fixed in or at a prescribed motion relative to the laboratory frame. The last 15 years witnessed significant development in the Lagrangian viewpoint, i.e., following ``tracer particles'' that move with the fluid in the turbulent flow field. The new perspective revealed many interesting properties of turbulence and advanced our understanding, but also posed intriguing questions. In this talk, I will review the basic understanding of turbulence (Kolmogorov's 1941 theory) and more recent development, and introduce some interesting problems currently under investigation.

Biographical sketch of Haitao Xu:

Dr. Haitao Xu is currently a Professor in the Center for Combustion Energy (CCE), Department of Thermal Engineering, Tsinghua University. Currently his main interest of research include the properties of fluid turbulence, especially from the Lagrangian perspectives, the interaction between turbulence and additives, such as particles and polymers. Dr. Haitao Xu studied at Huazhong University of Science and Technology, Wuhan, China (BE, 1993, PhD, 1998) and Cornell University, Ithaca, NY, USA (PhD, 2003). From 2003 to 2006, carried out post-doctoral research at Cornell University. From 2006 to 2014, he was a senior scientist and a research group leader at Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany, where his research focused on the Lagrangian properties of fluid turbulence.