Turbulent mixing induced by Richtmyer–Meshkov instability (RMI) in convergent geometry widely exists in natural phenomena and in engineering applications. In the present work, high-resolution numerical simulations of RMI at a complete cylindrical interface, with the imploding shock wave initially passing from the heavy fluid to the light fluid, are presented. Two different initial perturbations are applied. The mixing zone finally reaches a convergence ratio Cr ≈ 1.6 in both cases. Compared to classical RM instability, the more complex wave system, as well as the geometrical effect induced by the radial movement of mixing fluid, modifies the evolution of the mixing zone. The growth rate of the mixing width is analyzed in terms of the stretching or compression effect and species-penetration effect. In a cylindrical geometry, the stretching or compression effect is mainly induced by the wave system and the nonplanar geometric environment. The late-time turbulent mixing width induced by the penetration effect scales as (t−t0)θ, as with the evolution of planar RMI. For both cases, the mass-fraction profiles are collapsed at the late time if the radial coordinate is first shifted with the spike-front position and then scaled by the mixing width. By analyzing the distribution of the bubble (spike) contour, the dominant bubble (spike) diameter [D¯b(s)] is obtained. The ratios [βb(s)] between the dominant bubble (spike) diameter and the bubble (spike) amplitude [Wb(s)] are calculated, and a stable ratio of spike βs is observed during the late stage. Meanwhile, the ratio of the bubble βb is greater than 1 at late time.

Richtmyer–Meshkov (RM) instability in convergent geometries (such as cylinders and spheres) plays a fundamental role in natural phenomena and engineering applications, e.g. supernova explosion and inertial confinement fusion. Convergent geometry refers to a system in which the interface converges and the fluids are compressed correspondingly. By applying a decomposition formula, the stretching or compression (S(C)) effect is separated from the perturbation growth as one of the main contributions, which is defined as the averaged velocity difference between two ends of the mixing zone. Starting from linear theories, the S(C) effect in planar, cylindrical and spherical geometries is derived as a function of geometrical convergence ratio, compression ratio and mixing width. Specifically, geometrical convergence stretches the mixing zone, while fluid compression compresses the mixing zone. Moreover, the contribution of geometrical convergence in the spherical geometry is more important than that in the cylindrical geometry. A series of cylindrical cases with high convergence ratio is simulated, and the growth of perturbations is compared with that of the corresponding planar cases. As a result, the theoretical results of the S(C) effect agree well with the numerical results. Furthermore, results show that the S(C) effect is a significant feature in convergent geometries. Therefore, the S(C) effect is an important part of the Bell–Plesset effect. The present work on the S(C) effect is important for further modelling of the mixing width of convergent RM instabilities.

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