DFG - Priority Programme 1881: Turbulent Superstructures

The classical picture of turbulence which has prevailed since the pioneering works by Kolmogorov from the first half of the last century is that turbulent fluid motion is characterized by a cascade of vortices and swirls of different sizes that give rise to a featureless and stochastic fluid motion. Our daily experience shows, however, that turbulent flows in nature and technology are often organized in prominent large-scale and long-living structures that can cause extreme fluctuations. The focus of the present proposal are superstructures, i.e., patterns whose coherence does not stop at the natural scale, such as the boundary layer height, but extends over much larger scales. When present, superstructures dominate the global transport of mass, heat and momentum, they act as barriers to transport, and they increase the variability and fluctuations in the flow. Given the importance of superstructures for turbulent flows, we know very little about their origins, their dynamics, and their impact on turbulent flow properties. Furthermore, their consequences for the statistical properties of turbulent flows, and their connection to the occurrence of extreme events are poorly understood. It is likely that a better grasp of the physics of superstructures will lead to a better understanding of transport processes in many technological applications such as gas pipes or flows around ships and airplanes, as well as flows in the atmosphere or the ocean. Control strategies that take superstructures and their dynamics into account can result in new methods that reduce the drag of ships and airplanes or enhance the mixing in large industrial devices. The study of superstructures is now possible due to significant advances in measurement techniques, numerical simulation, and mathematical characterization. Tomographic laser-based measurement techniques can track the dynamics of turbulent structures with unprecedented resolution in space and time. Direct numerical simulations on massively parallel supercomputers have advanced to a level where turbulent flows in extended domains can be simulated at sufficiently high Reynolds numbers and in parameter ranges where superstructures emerge. Efficient methods to characterize dominant vortices and flow structures and to determine the transport across their boundaries as well as their dynamical evolution have been developed in applied mathematics. Computer science provides efficient algorithms for the visualization of structures in very large data sets. Within the priority program we propose to bring these different activities together and to coordinate them in a joint, interdisciplinary effort to unravel the mysteries of superstructures and to arrive at a quantitative characterization of their properties. The priority program will integrate engineers, physicists, applied mathematicians and computer scientists in order to study turbulent superstructures in laboratory experiments and large-scale simulations. The projects will aim

  • to unravel the origin of superstructures and the mechanics of their formation

  • to quantify the fluxes of mass, heat and momentum across the evolving interfaces, and the overall impact of superstructures on global transport and turbulence statistics

  • to develop approaches for the control and the efficient modeling of turbulent superstructures

  • to develop reliable measures for short-term forecasts of extreme events in high-Reynolds number turbulence