Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
复制标题
三维湍流的双曲性、阴影方向和敏感性分析
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
Angxiu Ni
中科院分区：
文献类型：
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作者：
Angxiu Ni
本文用可压缩流动模拟方法分析了雷诺数为525、马赫数为0.1的弱湍流三维圆柱绕流的双曲性、阴影方向和敏感性。通过计算前40个协变李雅普诺夫向量（CLVs），我们发现，不稳定的CLVs是活跃的近尾区，而稳定的CLVs是活跃的远尾区。这种现象与双曲性有关，因为它表明CLV指向不同的方向;它还表明，对于开放流，有很大一部分CLV是稳定的。然而，由于额外的中性CLV和CLV之间偶尔的相切，我们的系统是不一致的双曲。利用非侵入式最小二乘阴影算法，计算了长时间平均目标的阴影方向和灵敏度。我们的研究结果表明，跟踪方法可能是有效的一般混沌流体问题。
This paper uses compressible flow simulation to analyse the hyperbolicity, shadowing directions and sensitivities of a weakly turbulent three-dimensional cylinder flow at Reynolds number 525 and Mach number 0.1. By computing the first 40 covariant Lyapunov vectors (CLVs), we find that unstable CLVs are active in the near-wake region, whereas stable CLVs are active in the far-wake region. This phenomenon is related to hyperbolicity since it shows that CLVs point to different directions; it also suggests that for open flows there is a large fraction of CLVs that are stable. However, due to the extra neutral CLV and the occasional tangencies between CLVs, our system is not uniform hyperbolic. By the non-intrusive least-squares shadowing (NILSS) algorithm, we compute shadowing directions and sensitivities of long-time-averaged objectives. Our results suggest that shadowing methods may be valid for general chaotic fluid problems.