Deflection, drift, and advective growth in variable-density, laminar mixing layers

Specific features of the variable-density mixing layers without gravity effects are studied using self-similar solutions to the laminar and time-evolving variant of this flow. Density variations come from either mass or temperature mixing, accounting for, in the latter case, the effect of the Mach number. The transverse profiles of the flow quantities, as well as the time evolutions of the global characteristic scales of the mixing layer, are given for a wide range of density ratio and Mach-number values. When compared to the constant-density case, it appears that most of the specificity of these flows comes from the emergence of a nonzero transverse component of the velocity. First, it produces a deflection of the flow that can be either confined in the core of the layer or global, the whole layer being tilted at an angle from the initial flow direction. In most cases, this deflection is such that some part of the higher-density fluid is "entrained" in the direction of the lower-density fluid, leaving no possibility to define a dividing streamline. Second, it leads to a shift between the density profile and the profiles of the other flow quantities. This shift scales on the time-increasing mixing-layer thickness and therefore appears as a time drift. When global deflection is present, the tilting of the layer can be shown to be equivalent to a global drift of the mixing/shear layer toward the light-fluid side of the flow. Third, transport by the transverse velocity component affects the spreading of the mixing layer, giving rise to an additional effect referred to as advective growth. Examination of the density-ratio and Mach-number effects leads to surprising results: While the momentum thickness is always observed to decrease when increasing these parameters, conventional thicknesses based on the profiles of the different variables can show opposite behaviors depending on the form of the diffusion model for the considered variable