多孔弹性系统中多峰流动强迫的拉格朗日复杂性持续存在
Lagrangian complexity persists with multimodal flow forcing in poroelastic systems
摘要：
我们扩展以前的分析的起源复杂的输运动力学在多孔弹性介质的情况下，在边界处的输入瞬态信号是由一个多模态谱。通过添加谐波和非谐波模态频率作为扰动的基本模式，我们研究如何影响这种多模态信号的拉格朗日复杂性的多孔弹性流动。虽然结果适用于所有的多孔弹性介质（工业，生物和地球物理），具体来说，我们沙发上的讨论，在未抽水的沿海地下水系统的排放边界迫使潮汐。特定的局部区域的电导率场产生的马鞍，持有和编织（混合）的轨迹，导致在潮汐边界附近的地下水停留时间分布和拓扑混合流形的意外行为。虽然增加谱复杂度可以减少周期点的出现，特别是对于具有长特征周期的非调和谱，但拉格朗日复杂度的其他特征仍然存在。非均匀含水层中承压地下水流的自然多模态潮汐信号的作用可以引起与地下水排放过程的传统概念截然不同的外来流拓扑结构和混合效应。两者合计，我们的研究结果意味着，增加频谱复杂性的结果在更复杂的拉格朗日结构的流动通过多孔弹性介质。
英文摘要：
We extend previous analyses of the origins of complex transport dynamics in poroelastic media to the case where the input transient signal at a boundary is generated by a multimodal spectrum. By adding harmonic and anharmonic modal frequencies as perturbations to a fundamental mode we examine how such multimodal signals affect the Lagrangian complexity of poroelastic flow. While the results apply to all poroelastic media (industrial, biological and geophysical), for concreteness we couch the discussion in terms of unpumped coastal groundwater systems having a discharge boundary forced by tides. Particular local regions of the conductivity field generate saddles that hold up and braid (mix) trajectories, resulting in unexpected behaviours of groundwater residence time distributions and topological mixing manifolds near the tidal boundary. While increasing spectral complexity can reduce the occurrence of periodic points, especially for anharmonic spectra with long characteristic periods, other signatures of Lagrangian complexity persist. The action of natural multimodal tidal signals on confined groundwater flow in heterogeneous aquifers can induce exotic flow topologies and mixing effects that are profoundly different to conventional concepts of groundwater discharge processes. Taken together, our results imply that increasing spectral complexity results in more complex Lagrangian structure in flows through poroelastic media.
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