Baroclinic vorticity generation near the turbulent/ non-turbulent interface in a compressible shear layer

Abstract

Direct numerical simulations of temporally evolving compressible mixing layers are performed to study the baroclinic vorticity generation due to the interaction between the intense vorticity structures (IVSs) and the turbulent/non-turbulent interface (TNTI). In order to examine this interaction, the vorticity transport across the TNTI and the IVSs in compressible turbulence are studied. The conditional mean budget of different terms in the transport equation of vorticity with respect to the distance from the TNTI is analyzed in the interface coordinate system. In highly compressible mixing layers, it is shown that in proximity of the TNTI, contribution of the baroclinic torque to the total change of vorticity, compared with the other terms in the transport equation of the vorticity, cannot be ignored. The conditional average of the baroclinic torque in the vorticity transport equation reaches a maximum inside the interface layer, with the thickness of approximately one Taylor length scale, at a distance approximately equal to the radius of the IVS from the TNTI. Flow visualization results show that the intense vorticity structures generate a baroclinic torque as they become close to the turbulent/non-turbulent interface. In order to statistically examine the organized interaction between the TNTI and the IVSs, an algorithm described in the Appendix is developed to detect and to study the intense vorticity structures. It is shown that the IVSs generate a pressure gradient from the core of the vortex, low pressure, towards the region outside of the vortex. As the IVSs interact with the TNTI, the pressure gradient vectors become misaligned with the density gradient vectors, which are aligned with the direction normal to the TNTI, and generate a baroclinic torque. It is also observed that compressibility has a small effect on the structural features of the IVSs in the shear layer.