Mean profiles for a passive scalar in wall-bounded flows from symmetry analysis

Abstract

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Quantifying wall turbulence via a symmetry approach: a Lie group theory

“…We then carry out a Lie-group analysis on the (unclosed) mean momentum equation (MME) and construct a series of new invariant solutions. However, it is different from previously reported Lie-group analysis of the RANS equation by [25], [26] and [27], in which the mean velocity is systematically taken as the invariant variable. In our view, due to fluctuations, the mean velocity itself has broken most Lie group invariance, which is at best restored in very restricted domains.…”

Logarithmic scaling for fluctuations of a scalar concentration in wall turbulence

“…To obtain some constant value for C θ 2 , the amplitude |f Θ+θ | of the function f Θ+θ has to be ∝ 1/N in Eq. (10).…”

“…(3b) is in accordance with the existence of the characteristic concentration θ * and with the nonexistence of any characteristic constant in units of length. These two are the necessary and sufficient conditions for the logarithmic scaling of the average Θ(z) [10]. Since they are not sufficient for the variance θ 2 (z) (see Sec.…”

“…Within the constant-flux sublayer, θw(z) does not vary and leads to a characteristic constant θ * = θw /u * . Since Θ(z) − Θ 0 obeys a relation d(Θ−Θ 0 )/dz = dΘ/dz ∝ θ * /z [1], which is exclusively invariant under any shift of Θ 0 [10], we have…”

Transition in the asymptotic suction boundary layer over a heated plate

“…The interaction between shear and convection has been studied in boundary layers (Sparrow & Cess 1961;Merkin 1972), where it affects the functional form of the profile (Marati et al 2006). The dynamics of plumes and other structures has been investigated in the context of RB flows (Ahlers et al 2009;Chillà & Schumacher 2012) because of their contribution to the heat transport (Zocchi et al 1990;Parodi et al 2004;Zhou et al 2007;Zhou & Xia 2010).…”