Momentum transport process in the quasi self-similar region of free shear mixing layer

Abstract

In this study, we performed a direct numerical simulation (DNS) of a spatially developing shear mixing layer covering both developing and developed regions. The aim of this study is to clarify the driving mechanism and the vortical structure of the partial counter-gradient momentum transport (CGMT) appearing in the quasi self-similar region. In the present DNS, the self-similarity is confirmed in x/L ≥ 0.67 (x/δU0 ≥ 137), where L and δU0 are the vertical length of the computational domain and the initial momentum thickness, respectively. However, the trend of CGMT is observed at around kδU = 0.075 and 0.15, where k is the wavenumber, δU is the normalized momentum thickness at x/L = 0.78 (x/δU0 = 160), and kδU = 0.075 corresponds to the distance between the vortical/stretching regions of the coherent structure. The budget analysis for the Reynolds shear stress reveals that it is caused by the pressure diffusion term at the off-central region and by −p(∂u/∂y)¯ in the pressure-strain correlation term at the central region. As the flow moves toward the downstream direction, the appearance of those terms becomes random and the unique trend of CGMT at the specific wavenumber bands disappears. Furthermore, we investigated the relationship between the CGMT and vorticity distribution in the vortex region of the mixing layer, in association with the spatial development. In the upstream location, the high-vorticity region appears in the boundary between the areas of gradient momentum transport and CGMT, although the high-vorticity region is not actively producing turbulence. The negative production area gradually spreads by flowing toward the downstream direction, and subsequently, the fluid mass with high-vorticity is transported from the forehead stretching region toward the counter-gradient direction. In this location, the velocity fluctuation in the high-vorticity region is large and turbulence is actively produced. In view of this, the trend of negative production appears in the flow where the turbulence production and non-turbulent regions mix. Then, the non-turbulent region and CGMT almost simultaneously disappear in the fully developed region.