The Richtmyer-Meshkov instability (RMI) of single-mode air-${\mathrm{SF}}_6$ interfaces is studied numerically and the emphasis is placed on the effect of the principal curvature on the early evolution of the shocked interface. Two three-dimensional initial interfaces with opposite ($3\mathrm{D}-$) and identical (3D+) principal curvatures and a traditional two-dimensional interface (2D) are considered. The weighted essentially nonoscillatory scheme and the Level-Set method combined with the real ghost fluid method are adopted. For comparison, perturbations on the initial interfaces with the same wavelength and amplitude in the symmetry plane are employed. The numerical results confirm the experimental finding that the growth rate of perturbations in the symmetry plane at the linear stage in the $3\mathrm{D}-$ case is much smaller than that in the 2D and 3D+ cases. The difference among them can be ascribed to the different pressure and vorticity distributions associated with the principal curvatures of the initial interface. On the one hand, the high-pressure zones in the vicinity of the deformed interface are significantly different for three cases especially in the very beginning. The shock convergence and divergence at the interface are more severe in the 3D+ case than those in the 2D case, while the wave pattern in the $3\mathrm{D}-$ case is more complex. On the other hand, the baroclinic vorticity distribution plays a leading role in the interface deformation of the 3D RMI after the passage of the planar shock. The accumulated vorticity changes the movement of the deformed interface and makes the local growth of perturbations different among three cases.

• Received 28 November 2015
• Revised 21 January 2016

DOI:https://doi.org/10.1103/PhysRevE.93.023110