New Turbulent scaling laws arising from new statistical symmetries of the multi-point equations

Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations two new kinds of fundamental symmetries have been discovered. One of these symmetries was first observed for parallel wall-bounded shear flows in Khujadze and Oberlack (2004) though there this property only holds true for the two-point equation. Presently using this extended set of Lie symmetry groups a much wider class of invariant solutions or turbulent scaling laws can be derived for plane wall-bounded shear flow and decaying turbulence only employing first principles. In fact, the two presented applications can only be conceived from MPC equations using the new symmetries