Lagrangian Complexity Persists with Multimodal Flow Forcing in Compressible Porous Systems

Abstract

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.