Lagrangian Complexity Persists with Multimodal Flow Forcing in Compressible Porous Systems
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Lagrangian Complexity Persists with Multimodal Flow Forcing in Compressible Porous Systems M. G. Trefry1 · D. R. Lester2 · G. Metcalfe3 · J. Wu2 Received: 23 April 2020 / Accepted: 24 September 2020 © Springer Nature B.V. 2020
Abstract We extend previous analyses of the origins of complex transport dynamics in compressible porous 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 flow in compressible porous media. 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 compressible porous media. Keywords Compressible · Multimodal spectra · Lagrangian · Topology · Chaos
1 Introduction It has long been recognized that unsteady groundwater flows admit a range of behaviours that are critical to the transport and fate of dissolved contaminants in the subsurface (Weeks and Sposito 1998). Understanding these behaviours at the representative elemental volume scale is a topic of continuing interest. Due to the unsteady nature of these * M. G. Trefry [email protected] 1
Independent Researcher, Floreat, WA, Australia
2
School of Engineering, RMIT, Melbourne, VIC, Australia
3
School of Engineering, Swinburne University of Technology, Hawthorn, VIC, Australia
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flows, it is difficult to detect and understand the corresponding transport structures in the Eulerian frame. The Lagrangian approach is of more relevance here as it provides a convenient framework for detecting and classifying kinematic features that can control fluid mixing, segregation, discharge (and even chaotic) phenomena in porous media in the low Reynolds number regime. Together, these kinds of transport phenomena describe complex Lagrangian structures which engender potentially profound impacts on solute migration and reaction (Toroczkai et al. 1998; Tél et al. 2005; Valocchi et al. 2019). Building on e
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