Transport and structure formation in turbulent Rayleigh-Bénard-, Taylor-Couette- and pipe flows near solid walls

Description of turbulent flows is still a challenging problem in the engineering sciences and classical physics. The large spatiotemporal fluctuations and the couplings between structures on different length and time scales limit the velocity profiles provided by the fully nonlinear simulations already existent and open new directions in the turbulence modelling. Only few simple ideal cases have exact analytical solutions. The interactions between structures at many scales dominate especially in the vicinity of the solid walls. Based on the Ludwig Prandtl boundary layer theory, refined by symmetry considerations, important statements about mean velocity profiles have been already obtained. However, there are a lot of important problems which remain still unsolved. Thus, for the calculation of the heat flux in thermal convection, the predictions on profiles and scaling laws show uncertainties of some order of magnitudes. In our DFG-Research Unit, in the frame of the boundary-layer dynamics will be examined the global scaling properties of turbulent transport as well as the local dynamic processes in the vicinity of the solid walls. We expect a significant progress given by a comparative analysis of the three fundamental flows that have been mostly separately studied: thermal convection in a cell heated from below (Rayleigh-Bénard), shear turbulence between two concentric rotating cylinders (Taylor-Couette), and pressure-driven turbulence in a pipe flow. Our work will clarify the global laws of turbulent transport and will open new perspectives how to control the dynamics of near-wall turbulence and develop simple models for describing complex turbulent flows.

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