On the iso-surface transport equation in a turbulent, temporally developing mixing layer*

The iso-surface area density, Σ, and its transport equation can be used to describe turbulent mixing phenomena that involve a sharp interface in the flow, e.g., the premixed or non-premixed flame surface, the mixing of turbulent fluids into non-turbulent environments, or even the mixing of pollutants in the atmosphere or ocean. Importantly, the iso-surface area density is defined in terms of an iso-value of a scalar field, such as the progress variable for premixed combustion (usually in terms of temperature or species mass fraction), the mixture fraction for non-premixed combustion, or the magnitude of vorticity for the turbulent/non-turbulent interface. Due to computational and experimental limitations, little is known about the evolution and transport of Σ in non-homogeneous turbulence. In this study, each term of the evolution equation of Σ is investigated based on the direct numerical simulation (DNS) of a turbulent, temporally developing mixing layer. These investigations suggest that, during the self-similar period of the mixing layer growth, in which Σ and the terms in its equation also behave in a self-similar manner, the rate-of-change of Σ and the turbulent flux term scale with hλ_φ/?U , where h is the width of the mixing layer, λ_φ is the scalar Taylor length scale, and ?U is the velocity difference across the mixing layer. It is found that the production and destruction terms scale with an additional factor of (ReSc)^1/2 compared to the rate-of-change and turbulent flux terms, and analogously that the molecular diffusion term scales with a factor of (ReSc)^−1/2 compared to the rate-of-change and turbulent flux terms.