Nonlinear saturation amplitudes in classical Rayleigh-Taylor instability at arbitrary Atwood numbers
Nonlinear saturation amplitudes in classical Rayleigh-Taylor instability at arbitrary Atwood numbers
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DOI：
10.1063/1.3702063
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发表时间：
2012-04
影响因子：
2.2
通讯作者：
Wanhai Liu;L. F. Wang;W. Ye;Xiantu He
中科院分区：
文献类型：
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作者：
Wanhai Liu;L. F. Wang;W. Ye;Xiantu He
在这项研究中，在瑞利-泰勒不稳定性（RTI）的前两个谐波的非线性饱和振幅（NSAs）的无旋，不可压缩，和无粘流体，在任意Atwood数的不连续的配置文件，分析研究，通过考虑非线性校正到十阶。基模的NSA被定义为当基模（第一谐波）的增长与其对应的线性增长相比减少10%时，在饱和时间的基模的线性（纯指数）增长幅度。二次谐波的NSA可以用同样的方法得到。分析结果表明，高阶校正效应和阿特伍德数效应对RTI的负散射效应起着重要作用。结果表明，随着A的增加，基模的NSA减小。当考虑高阶次谐波效应时，基模的非对称散射比以前文献在三阶微扰理论框架下的预测值大得多[J. W.雅各布斯和我。Catton，J. Fluid Mech.187，329（1988）; S. W.哈安，Phys. Fluids B 3，2349（1991）]。我们发现，二次谐波的NSA随着A的增加首先迅速下降，达到一个最小值，然后缓慢增加。此外，前两个谐波的NSA表现出随着修正阶数的增加而收敛的趋势。因此，在消极安全保证发挥作用的应用中，如惯性约束聚变点火靶设计中，应包括这一点。
In this research, nonlinear saturation amplitudes (NSAs) of the first two harmonics in Rayleigh-Taylor instability(RTI) for irrotational, incompressible, and inviscid fluids, with a discontinuous profile at arbitrary Atwood numbers, are investigated analytically, by considering nonlinear corrections up to the tenth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth. The NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the higher-order correction (HOC) and the Atwood number (A) play an important role in the NSA of the RTI. It is found that the NSA of the fundamental mode decreases with increasing A. And when the HOC effects are considered, the NSA of the fundamental mode is significantly larger than the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. We find that the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the NSAs of the first two harmonics demonstrate the trend of convergence as the order of corrections increases. Thus, it should be included in applications where the NSAs play a role, such as inertial confinement fusion ignition target design.