Shearless turbulent/nonturbulent mixing has primarily been explored in the incompressible limit for nominally planar interfaces. In this work, we investigate compressible and geometrical effects on turbulent/nonturbulent mixing in the absence of a mean shear. Focusing on initially homogeneous isotropic turbulence adjacent to a quiescent fluid, we theoretically predict the evolution of the mixing region width and turbulent kinetic energy and validate these predictions using direct numerical simulation. For the planar case, we find that the mixing region grows as a power law in time ($\sim t^{2/3}$), consistent with incompressible theory. However, we demonstrate that the turbulent kinetic energy is affected by energy transport away from the mixing region due to dilatation, in addition to viscous dissipation. We establish the dependence of the time evolution of the turbulent kinetic energy on the parameters governing the problem (Taylor scale, rms velocity, and initial dilatation). Dilatation leads to an increased decay rate of turbulent kinetic energy. When considering a cylindrical geometry, the mixing region growth is self-similar with the mixing region width exhibiting a power-law dependence in time as $t^{1/2}$. The scaling for the turbulent kinetic energy decay can also be extended to include energy transport away from the mixing region by dilatation and taking into account the diverging geometry.

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• Compressible turbulence
• Turbulent mixing