Obstacle-Controlled Lagrangian Pathways and Fate in Low-Volume Lock-Exchange Gravity Currents

Finite-volume gravity currents frequently encounter bottom obstacles, particularly in underwater environments such as lakes and oceans. However, how obstacle–current interactions reorganize Lagrangian transport pathways and ultimately determine the fate of fluid elements over the full current life cycle remains unclear. Using large-eddy simulations, we focus on a low-volume lock-exchange gravity current impinging on an isolated two-dimensional triangular obstacle. Fluid-element trajectories are tracked from collapse through propagation, obstacle interaction, and final dilution and decay, and are classified using K-means clustering into five transport modes linked to characteristic flow structures. We find that increasing obstacle slenderness strengthens upstream reflection and reduces downstream overflow, thereby shifting the fate of tracer particles from downstream delivery toward upstream retention. In addition, the obstacle standoff distance controls the dynamical state of the current at impact, producing systematic yet non-monotonic changes in the fractional population of the transport modes. This study establishes an explicit correspondence between evolving flow structures and clustered Lagrangian pathways. Comparative cases with varying geometric configuration, density contrast, flow depth, and release volume indicate that the identified transport patterns are reasonably robust. Therefore, the present results provide a fate-oriented predictive framework and theoretical basis for the transport of finite-volume gravity currents near obstacles, with important implications for engineering applications.