Dispersion on laminar and turbulent network flow

Karst aquifers are highly dynamic and heterogeneous systems, where solutes can be transported rapidly through conduit networks while parts of the contaminant mass temporarily reside in immobile zones, resulting in complex transport behavior and prolonged tailing in breakthrough curves. Accurately predicting solute dispersion in these systems remains challenging due to their multiscale structure and highly variable flow dynamics. To investigate these processes, flow in synthetic karst networks and in the real conduit system of the Seefeldhöhle (Switzerland) is simulated using a graph-based Laplacian solver capable of capturing both laminar and turbulent conditions. Solute transport is modeled using a Time-Domain Random Walk (TDRW) particle tracking approach. Particular attention is given to the role of mixing at conduit intersections, where both complete-mixing and streamline-routing rules are implemented to assess their influence on longitudinal and transverse dispersion. Transport behavior is characterized through first passage time distributions, particle visitation maps, and spatial moments. To further analyze the structure of particle velocities along trajectories, Lagrangian speed series are derived and their dependence structure is quantified using speed copulas. This analysis reveals distinct forms of correlation and intermittency that govern spreading, breakthrough tailing, and the sensitivity to network heterogeneity. While specific mixing processes at intersections affect local dispersion patterns, bulk metrics such as breakthrough curves and spatial moments remain comparatively insensitive. Building on these findings, the framework will be extended toward a multiscale upscaling approach based on a Continuous-Time Random Walk (CTRW), aiming to link conduit-scale velocity statistics with emergent network-scale transport dynamics.