DOI: 10.1615/TSFP7
TURBULENT SCALING LAWS AND WHAT WE CAN LEARN FROM THE MULTI-POINT CORRELATION EQUATIONS
SINOPSIS
We presently show that the infinite set of multi-point correlation equations, which are direct statistical consequences of the Navier-Stokes equations, admit a rather large set of Lie symmetry groups. This set is considerable extended compared to the set of groups which are implied from the original set of equations of fluid mechanics. Specifically a new scaling group and translational groups of the correlation vectors and all independent variables have been discovered. These new statistical groups have important consequences on our understanding of turbulent scaling laws to be exemplarily revealed by two examples. Firstly, one of the key foundations of statistical turbulence theory is the universal law of the wall with its essential ingredient is the logarithmic law. We demonstrate that the log-law fundamentally relies on one of the new translational groups. Furthermore, we consider a rotating channel flow, whose scaling behavior can only be described using the new statistical symmetries. It can be seen that the direction of rotation axes plays an important role, because different axes result in very different scaling laws.