This paper investigates the growth of perturbations on the inner surface of a dense imploding spherical shell due to hydrodynamic instabilities. The perturbations change in amplitude due to Richtmyer–Meshkov instability and Rayleigh-Taylor instability, geometric convergence, and compressibility. Two mode numbers ($\ell =5,50$) and three different perturbation amplitudes ($a_0=0.1\lambda ,0.01\lambda ,0.001\lambda$) are applied to the surface of the dense inner shell. Two independent codes were used to perform simulations with these six perturbation profiles at four convergence ratios, ranging from 3.6 to 7.3, for a total of 48 cases. The mixing layer amplitudes show good agreement between the two simulation codes across the range of convergence ratios, mode numbers, and initial amplitudes. The growth of the mixing layer is employed to validate an extension of a recently proposed Bell-Plesset model, showing good agreement across the range of convergence ratios. Persistent and substantial shock-deposited fluctuating kinetic energy is observed within the light core, away from the perturbed interface. Temporal evolution of fluctuating kinetic energy indicates a time delay between the peak radial and theta directions, consistent with a build-up of vortical motion. A “jet” like phenomena is observed at the peaks and troughs of the initial perturbations in both simulation codes across a variety of cases. It is postulated that these occur due to the shape singularity shown to develop in spatially periodic perturbed planar shock waves in ideal gas dynamics. Significant anisotropy of kinetic energy components is present at all times.

本文研究了由于流体动力不稳定性而在稠密内爆球壳内表面上扰动的增长。由于Richtmyer-Meshkov不稳定性和Rayleigh-Taylor不稳定性，几何收敛和可压缩性，摄动幅度发生变化。两个模式编号（$\ell =5，50$）和三个不同的摄动幅度（${\mathrm{一种}}_0=0.1\lambda ，0.01\lambda ，0.001\lambda$）涂在致密内壳的表面上。使用两个独立的代码对这六个摄动曲线以3.6至7.3的四个收敛比率进行仿真，总共48个案例。在收敛比，模数和初始振幅的范围内，混合层的振幅在两个仿真代码之间显示出良好的一致性。混合层的增长用于验证最近提出的Bell-Plesset模型的扩展，在收敛比率范围内显示出良好的一致性。在光芯内，远离扰动的界面，观察到持久且大量的震荡波动动能。动能波动的时间演变表明峰值径向和theta方向之间存在时间延迟，与涡旋运动的形成相一致。在各种情况下，在两种模拟代码中的初始扰动的波峰和波谷处都观察到“喷射”现象。据推测，这些现象是由于形状奇异性的出现而产生的，这种奇异性是在理想气体动力学中在空间周期性扰动的平面激波中形成的。动能分量始终存在明显的各向异性。