3D Topological Relations in Double-Holed Complex Bodies for Shoal-Bar System Evolution

Abstract. The dynamic evolution of shoal-bar systems in fluvial geomorphology remains challenging to fully capture through conventional observation methods. While multi-dimensional dynamic data enables qualitative analysis of riverine morphology, existing approaches lack effective spatiotemporal topological analysis. This study proposes a novel spatiotemporal modelling framework based on the topological invariance principles of three-dimensional perforated complexes. Focusing on the connectivity preservation in river systems under rotational and scaling transformations, we develop a dual-cavity complex topology model to characterize the dynamic transitions between shoals and sandbars. Compared with traditional single-cavity models, the proposed approach incorporates dynamic cavity features that precisely quantify thalweg elevation changes while resolving the spatiotemporal coupling mechanisms of bar morphology migration. Case study results demonstrate that this approach not only preserves spatial correlations among geomorphic elements but also enables evolutionary trend inversion through topological relation analysis. The methodology provides new theoretical foundations for developing digital twin watershed systems, offering enhanced capabilities for simulating complex fluvial processes.