通过非线性递归函数从二维湍流中获得的动力学相关递归流
Dynamically relevant recurrent flows obtained via a nonlinear recurrence function from two-dimensional turbulence
AI总结：
本文利用非线性三和弦诊断二维湍流直接数值模拟中的递归现象，并结合 Newton-GMRES-hookstep 提取多样的不稳定周期与相对周期轨道，用于湍流统计重构。
摘要：
本文展示了通过使用非线性三和弦来诊断直接数值模拟中的递归现象，从而从二维湍流中高效提取不稳定递归流。研究从模拟中识别出近递归片段，随后使用标准的 Newton-GMRES-hookstep 方法进行收敛，但与以往开展这种“递归流分析”的研究相比，所得结果具有更高的多样性。研究能够识别出不稳定周期轨道和相对周期轨道，这些轨道跨越更大的耗散率取值范围，即对应于极端爆发事件。研究发现，与复傅里叶振幅的标准欧几里得范数相比，三和弦变量为在此类轨道中活跃的更多种类空间模态提供了一种更自然的加权方式。此外，三和弦变量内置了对系统连续对称性的约化，从而在获得相对周期轨道时避免了对平移进行搜索的需要。借助这些轨道，本文研究了重构湍流统计量时的最优权重，并指出，事实上，只要展开中包含足够多的动力学相关轨道，基于解不稳定性的简单启发式加权就能提供非常好的预测。
英文摘要：
This paper demonstrates the efficient extraction of unstable recurrent flows from two-dimensional turbulence by using nonlinear triads to diagnose recurrence in direct numerical simulations. Nearly recurrent episodes are identified from simulations and then converged using a standard Newton- GMRES-hookstep method, however with much greater diversity than previous studies which performed this 'recurrent flow analysis'. Unstable periodic and relative periodic orbits are able to be identified which span larger values of dissipation rate, i.e. corresponding to extreme bursting events. The triad variables are found to provide a more natural way to weight the greater variety of spatial modes active in such orbits than a standard Euclidian norm of complex Fourier amplitudes. Moreover the triad variables build in a reduction of the continuous symmetry of the system which avoids the need to search over translations when obtaining relative periodic orbits. Armed with these orbits we investigate optimal weightings when reconstructing the statistics of turbulence and suggest that, in fact, a simple heuristic weighting based on the solution instability provides a very good prediction, provided enough dynamically relevant orbits are included in the expansion.
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