Effective Description of Superstructures in Turbulent Convection and Simple Turbulent Shear Flows

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Turbulent flows are a ubiquitous phenomenon in nature and often show a surprising large-scale order, even though turbulence is associated with small-scale fluctuations and chaotic, irregular motion. These large-scale structures in presence of turbulent fluctuations are one manifestation of so-called turbulent superstructures. Turbulent superstructures occur in a range of prototypical flows including wall-bounded and shear-driven flows as well as in convective flows. Turbulent convection has been at the center of our investigations in the first funding period. In our previous proposal we have pointed out that a predictive theory of large-scale flow patterns in the turbulent regime is currently lacking. On the one hand, this is due to the fact that dynamics of turbulent superstructures, and in particular the interaction of large-scale flow features and turbulence, so far was not well characterized. On the other hand, theoretical tools to develop an effective description of turbulent superstructures have been missing. As detailed below, we have made promising progress with respect to both of these challenges in the first funding period. In particular, we have gained a detailed understanding of the energy balance of large-scale flow features in Rayleigh-Bénard convection, and we have developed a heuristic reduced-order model to elucidate the role of small-scale fluctuations on large-scale pattern formation. The primary goal for the second funding period is to combine these approaches to achieve an effective description of superstructures in turbulent convection.As part of the collaborative research within the SPP we have closely collaborated with Juan Pedro Mellado and have applied our theoretical analysis to convective atmospheric flows, which we also plan to extend in the second funding period.Having gained a better understanding of superstructures in turbulent convection, we also plan to extend our investigations to a greater variety of turbulent flows, including shear flow turbulence, Taylor-Couette turbulence as well as pipe and channel flows. Such comparative analyses will help to shed light on potentially universal mechanisms and features in the generation of turbulent superstructures.