Applications of the new symmetries of the multi-point correlation equations

New symmetry-induced scaling laws of passive scalar transport in turbulent plane jets

“…Second, in every higher-moment equation, only one additional unclosed function appears. Besides, a general symmetry analysis of the TPC equations has resulted in additional symmetries compared with only those that are implied by Navier-Stokes equations (Oberlack & Rosteck 2010, 2011Avsarkisov et al 2014). These symmetries, which are denoted statistical symmetries, have been shown to play a key role in the understanding of the scaling laws in turbulent flows, especially for higher moments of the velocity.…”

“…Second, in every higher-moment equation, only one additional unclosed function appears. Besides, a general symmetry analysis of the TPC equations has resulted in additional symmetries compared with only those that are implied by Navier–Stokes equations (Oberlack & Rosteck 2010, 2011; Avsarkisov et al. 2014).…”

New scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

“…It is important to note that all of these symmetries of the Navier-Stokes equation transfer to the equations of the multi-point formulation (see e.g. Oberlack & Rosteck 2011). In addition to the symmetries stemming from the Navier-Stokes and the energy equations, an additional scaling group of all dependent variables is admitted, which was first discovered in Oberlack & Rosteck (2010), and later in Waclawczyk et al (2014) it was shown that this symmetry is a measure of intermittency.…”