Coordination Funds

• Applicant: Professor Dr. Jörg Schumacher
• Subject Area: Fluid Mechanics ; Mathematics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2016 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 316221523

The classical picture of turbulence 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 Priority Programme are Turbulent 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. 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 and fast processing of structures in very large data sets.The aim of the present Priority Programme is to integrate the different recent advances to arrive at a comprehensive characterization and understanding of turbulent superstructures. More detailed, this includes the experimental characterization of superstructures, direct numerical simulations of turbulent large-scale and superstructures, and their detection and identification by different Lagrangian and Eulerian methods. Furthermore, we want to analyse the origin of turbulent superstructures from primary and secondary instabilities, the role of symmetries and boundary conditions for their formation and dynamics. We want to understand their role for the turbulent transport, in particular that of their interfaces. Finally, we want to develop reduced models to describe their dynamics effectively and develop strategies to control these structures. In order to keep the program focused, it is intended to study singlephase, wall-bounded flows in simple Cartesian and parallel geometries, driven by shear or buoyancy. It is only by joining forces across the various disciplines that we will be able to achieve a better characterization of turbulent superstructures, to extract information about their essential properties and thus to obtain a comprehensive understanding of their impact on turbulence statistics and turbulent transport.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1881: Turbulent Superstructures