Vorticity Layer–Vortex Interaction, a Prelude to Understanding Entrainment

Toward understanding the entrainment mechanism across the turbulent non-turbulent interface, we explore numerically the interaction between a vortex rod adjacent and aligned with a vorticity layer (VL). An Oseen vortex (Re_Γ=1000) is positioned near the VL with a circulation per unit length of Re_s=1000. The VL thickness and the distance between the vortex center and VL are 1 and 2 times the vortex radius R, respectively. The increase in the vortical fluid volume is used to quantify the entrainment rate. When the vortex is orthogonal to the VL vorticity, the VL is distorted by the vortex, but the latter remains unperturbed. Additionally, in this configuration, large gradients of enstrophy enhance viscous diffusion and amplify the volume-integrated enstrophy 6 times the initial value. When VL and vortex vorticity vectors are parallel – hence no stretching or tilting – the entrainment rate is 11% less than when the vectors are orthogonal. Although vortex stretching dominates the interaction, there is, however, an initial transient entrainment rate reduction due to vorticity compression. Subsequently, a linear growth rate (1.8Γ/R²) of the enstrophy volume integral is acquired, dominated only by vortex stretching. Variation of enstrophy production both along and across VL is explained in terms of the induced velocity of the vortex.