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 in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the 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 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 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 and the advection term scale with, where is the width of the mixing layer, is the scalar Taylor length scale and is the velocity difference. The production and destruction terms are found to scale with an additional factor. In contrast, the molecular diffusion term is found to scale with a factor compared to. Importantly, it is found that the difference between the production and destruction terms, or net surface 'stretch', scales with the same factor as and the advection term, which may have a significant impact on how the evolution of is understood and modelled in turbulent flows.