Turbulent entrainment across turbulent-nonturbulent interfaces in stably stratified mixing layers

The entrainment process in stably stratified mixing layers is studied in relation to the turbulent-nonturbulent interface (TNTI) using direct numerical simulations. The statistics are calculated with the interface coordinate in an Eulerian frame as well as with the Lagrangian fluid particles entrained from the nonturbulent to the turbulent regions. The characteristics of entrainment change as the buoyancy Reynolds number Re-b decreases and the flow begins to layer. The baroclinic torque delays the enstrophy growth of the entrained fluids at small Re-b, while this effect is less efficient for large Re b. The entrained particle movement within the TNTI layer is dominated by the small dissipative scales, and the rapid decay of the kinetic energy dissipation rate due to buoyancy causes the entrained particle movement relative to the interface location to become slower. Although the Eulerian statistics confirm that there exists turbulent fluid with strong vorticity or with large buoyancy frequency near the TNTI, the entrained fluid particles circumvent these regions by passing through the TNTI in strain-dominant regions or in regions with small buoyancy frequency. The multiparticle statistics show that once the nonturbulent fluid volumes are entrained, they are deformed into flattened shapes in the vertical direction and diffuse in the horizontal direction. When Re b is large enough for small-scale turbulence to exist, the entrained fluid is able to penetrate into the turbulent core region. Once the flow begins to layer with decreasing Re b, however, the entrained fluid volume remains near the outer edge of the turbulent region and forms a stably stratified layer without vertical overturning.