Compressible vortex reconnection

Abstract

Reconnection of two antiparallel vortex tubes is studied as a prototypical coherent structure interaction to quantify compressibility effects in vorticity dynamics. Direct numerical simulations of the Navier-Stokes equations for a perfect gas are carried out with initially polytropically related pressure and density fields. For an initial Reynolds number (Re = Γ /v, circulation divided by the kinematic viscosity) of 1000, the pointwise initial maximum Mach number (M) is varied from 0.5 to 1.45. At M=0.5, not surprisingly, the dynamics are essentially incompressible. As M increases, the transfer of Γ starts earlier. For the highest M, we find that shocklet formation between the two vortex tubes enhances early Γ transfer due to viscous cross-diffusion as well as baroclinic vorticity generation. The reconnection at later times occurs primarily due to viscous cross-diffusion for all M. However, with increasing M, the higher early Γ transfer reduces the vortices’ curvature growth and hence the Γ transfer rate; i.e. for the Re case studied, the reconnection timescale increases with M. With increasing M, reduced vortex stretching by weaker ‘bridges’ decreases the peak vorticity at late times. Compressibility effects are significant in countering the stretching of the bridges even at late times. Our observations suggest significantly altered coherent structure dynamics in turbulent flows, when compressible.