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Secondary instability of the spike-bubble structures induced by nonlinear Rayleigh-Taylor instability with a diffuse interface
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-22 , DOI: 10.1103/physreve.104.035108 Lin Han 1 , Jianjie Yuan 1 , Ming Dong 2 , Zhengfeng Fan 3
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-22 , DOI: 10.1103/physreve.104.035108 Lin Han 1 , Jianjie Yuan 1 , Ming Dong 2 , Zhengfeng Fan 3
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Laminar-turbulent transition in Rayleigh-Taylor (RT) flows usually starts with infinitesimal perturbations, which evolve into the spike-bubble structures in the nonlinear saturation phase. It is well accepted that the emergence and rapid amplification of the small-scale perturbations are attributed to the Kelvin-Helmholtz-type secondary instability due to the high velocity shears induced by the stretch of the spike-bubble structures, however, there has been no quantitative description on such a secondary instability in literature. Moreover, the instability mechanism may not be that simple, because the acceleration or the “rising bubble” effect could also play a role. Therefore, based on the two-dimensional diffuse-interface RT nonlinear flows, the present paper employs the Arnoldi iteration and generalized Rayleigh quotient iteration methods to provide a quantitative study on the secondary instability. Both sinuous and varicose instability modes with high growth rates are observed, all of which are confirmed to be attributed to both the Rayleigh-Taylor and Kelvin-Helmholtz regimes. The former regime dominates the early-time instability due to the “rising bubble” effect, whereas the latter regime becomes more significant as time advances. Being similar to the primary RT instability [Yu et al., Phys. Rev. E 97, 013102 (2018), Dong et al., Phys. Rev. E 99, 013109 (2019), Fan and Dong, Phys. Rev. E 101, 063103 (2020)], the diffuse interface also leads to a multiplicity of the secondary instability modes and higher-order modes are found to exhibit more local extremes than the lower-order ones. Direct numerical simulations are carried out, which confirm the linear growth of the secondary instability modes with infinitesimal amplitudes and show their evolution to the turbulent-mixing state.
中文翻译：
具有扩散界面的非线性 Rayleigh-Taylor 不稳定性引起的尖峰气泡结构的二次不稳定性
Rayleigh-Taylor (RT) 流中的层流-湍流转变通常始于无穷小的扰动，在非线性饱和阶段演变为尖峰气泡结构。众所周知，小尺度扰动的出现和快速放大归因于由尖峰气泡结构拉伸引起的高速剪切引起的开尔文-亥姆霍兹型二次不稳定性，然而，没有文献中对这种二次不稳定性的定量描述。而且，不稳定的机制可能没有那么简单，因为加速或“上升的泡沫”效应也可能起作用。因此，基于二维扩散界面 RT 非线性流，本文采用 Arnoldi 迭代和广义瑞利商迭代方法对二次不稳定性进行了定量研究。观察到具有高增长率的蜿蜒和曲张不稳定性模式，所有这些都被证实归因于瑞利 - 泰勒和开尔文 - 亥姆霍兹制度。由于“泡沫上升”效应，前者主导了早期的不稳定，而后者随着时间的推移变得更加重要。类似于原发性 RT 不稳定 [Yu 由于“泡沫上升”效应，前者主导了早期的不稳定，而后者随着时间的推移变得更加重要。类似于原发性 RT 不稳定 [Yu 由于“泡沫上升”效应，前者主导了早期的不稳定，而后者随着时间的推移变得更加重要。类似于原发性 RT 不稳定 [Yu等。，物理。Rev. E 97 , 013102 (2018), Dong等人。，物理。Rev. E 99 , 013109 (2019), Fan and Dong, Phys. Rev. E 101 , 063103 (2020)]，扩散界面也导致了二次不稳定模式的多样性，并且发现高阶模式比低阶模式表现出更多的局部极值。进行了直接数值模拟，证实了具有无穷小振幅的二次不稳定模式的线性增长，并显示了它们向湍流混合状态的演变。
更新日期：2021-09-22
中文翻译：
具有扩散界面的非线性 Rayleigh-Taylor 不稳定性引起的尖峰气泡结构的二次不稳定性
Rayleigh-Taylor (RT) 流中的层流-湍流转变通常始于无穷小的扰动，在非线性饱和阶段演变为尖峰气泡结构。众所周知，小尺度扰动的出现和快速放大归因于由尖峰气泡结构拉伸引起的高速剪切引起的开尔文-亥姆霍兹型二次不稳定性，然而，没有文献中对这种二次不稳定性的定量描述。而且，不稳定的机制可能没有那么简单，因为加速或“上升的泡沫”效应也可能起作用。因此，基于二维扩散界面 RT 非线性流，本文采用 Arnoldi 迭代和广义瑞利商迭代方法对二次不稳定性进行了定量研究。观察到具有高增长率的蜿蜒和曲张不稳定性模式，所有这些都被证实归因于瑞利 - 泰勒和开尔文 - 亥姆霍兹制度。由于“泡沫上升”效应，前者主导了早期的不稳定，而后者随着时间的推移变得更加重要。类似于原发性 RT 不稳定 [Yu 由于“泡沫上升”效应，前者主导了早期的不稳定，而后者随着时间的推移变得更加重要。类似于原发性 RT 不稳定 [Yu 由于“泡沫上升”效应，前者主导了早期的不稳定，而后者随着时间的推移变得更加重要。类似于原发性 RT 不稳定 [Yu等。，物理。Rev. E 97 , 013102 (2018), Dong等人。，物理。Rev. E 99 , 013109 (2019), Fan and Dong, Phys. Rev. E 101 , 063103 (2020)]，扩散界面也导致了二次不稳定模式的多样性，并且发现高阶模式比低阶模式表现出更多的局部极值。进行了直接数值模拟，证实了具有无穷小振幅的二次不稳定模式的线性增长，并显示了它们向湍流混合状态的演变。
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