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

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

“…Townsend 1956; George 1989, 1992 a ), such that self-similarity of the turbulence quantities can be fully constructed. More details to justify this assumption can be found in Oberlack & Peters (1993), Lundgren (2003) and Sadeghi & Oberlack (2020).…”

“…(2015), Sadeghi et al. (2018) and Sadeghi & Oberlack (2020), the concept of TPC has become an important analytical tool in turbulence for two main reasons. First, it delivers additional information on the turbulence statistics such as length scale.…”

“…Finally, we should note that we construct the scaling laws from the TPC equations (2.10) and (2.11) while the viscous and diffusivity terms are neglected; that is, we consider only length scales that are way beyond the Kolmogorov and Corrsin–Obukhov scales, i.e. and (Sadeghi & Oberlack 2020). This is mainly because that for the statistical behaviour of turbulence at the limit of small viscosity, viscosity is almost always neglected (e.g.…”

“…2015; Sadeghi et al. 2018; Sadeghi & Oberlack 2020; Sadeghi, Oberlack & Gauding 2020). For example, they have studied the turbulent channel, the velocity field of a temporally evolving jet, the isotropic homogeneous turbulence and some other canonical wall-bounded and shear flows using Lie symmetry theory by investigating the infinite series of two-point correlation (TPC) and multi-point correlation equations.…”

“…Oberlack 2001; Oberlack et al. 2015; Sadeghi, Oberlack & Gauding 2018; Sadeghi & Oberlack 2020). Therefore, in this paper, we only briefly review a schematic of this method in Appendix A.…”