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, for example, the velocity correlations in homogeneous isotropic turbulence resulting from von Kármán-Howarth equation or the energy dissipation at upper boundaries for simple flow geometries. 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 in the large barrel from Ilmenau, 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, RB), shear turbulence between two concentric rotating cylinders (Taylor-Couette, TC), and pressure-driven turbulence in a pipe flow (RS).
For the global properties, will be investigated the transport of the momentum and the heat flux, for different geometries and system parameters. In the case of RB convection, such a global analysis has identified the Rayleigh and Prandtl numbers as leading parameters for different physical processes. The transfer of these considerations to TC-flow seems to be promising, because by varying the rotation rates of the inner and outer cylinders, the dynamics in the boundary layers and their contribution to the global transport properties can be noticeably changed.
For the local properties, the coherent structures and their dynamics are of main interest. For the turbulence transition in a pipe flow and also for plane Couette and Poiseuille flows, there are numerically found three-dimensional solutions of the Navier-Stokes equation in a very accurate way. These structures open the possibility of going beyond the description of statistical analysis of the kinematics and near-wall dynamics and to investigate their contribution to the global momentum and heat flux transfer.
The comparison between Rayleigh-Bénard, Taylor-Couette and pipe flows is possible through the recently identified corresponding transport and dissipation rates. We will expand the similitude found between RB and TC from the linear analysis to the turbulent area. By investigating the processes in three different systems for different Rayleigh and Reynolds numbers, we expect a rather complete coverage of the most important parameter ranges. Thus, our work will clarify the global laws of turbulent transport. In addition, this research will open new perspectives how to control the dynamics of near-wall turbulence and develop simple models for describing complex turbulent flows.