On the evolution of scalar iso-surface area density in a turbulent mixing layer

Abstract

In this study, the transport equation for scalar iso-surface area density ( $\varSigma$ ) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the $\varSigma$ transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that $\varSigma$ exhibits self-similar behaviour consistent with the development of the temporal mixing layer (Blakeley et al., J. Fluid Mech., vol. 951, 2022, A44). Accordingly, each of the terms in the $\varSigma$ transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of $\varSigma$ ( $\partial \varSigma /\partial t$ ) and the advection term scale with $h\lambda _\varPhi /\Delta U$ , where $h$ is the width of the mixing layer, $\lambda _\varPhi$ is the scalar Taylor length scale and $\Delta U$ is the velocity difference. The production and destruction terms are found to scale with an additional factor $({Re}\,Sc)^{1/2}$ . In contrast, the molecular diffusion term is found to scale with a factor $({Re}\,Sc)^{-1/2}$ compared to $\partial \varSigma /\partial t$ . Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as $\partial \varSigma /\partial t$ and the advection term, which may have a significant impact on how the evolution of $\varSigma$ is understood and modelled in turbulent flows.