A Multiscale Interpretation of Memory-Driven Anomalous Sediment Transport

Anomalous sediment transport is often observed in turbulent flows. Under these conditions, particle motion frequently deviates from the classical Fickian diffusion assumption due to long-term correlations and complex interactions between flow and sediment. Although many models have been developed to describe this behavior, it remains challenging to link particle-scale dynamics, field-scale transport processes, and statistical descriptions of concentration distributions within a single physical framework. As a result, parameters used in statistical or fractional-order models are often obtained through empirical fitting, and their physical interpretations remain unclear.

This study presents a multiscale framework for interpreting memory-driven anomalous sediment transport by linking particle dynamics, continuum transport behavior, and statistical descriptions. At the particle scale, a Fractional Sediment Diffusion Particle Tracking Model (FSDPTM) is employed to simulate sediment motion with temporal memory. Under this setting, anomalous diffusion emerges from non-Markovian particle dynamics. The mean-square displacement (MSD) is then analyzed to quantify anomalous transport behavior at the particle scale and to describe the strength of temporal correlations.

At the macroscopic scale, transient concentration fields obtained from particle trajectories are used to guide the fractional advection–diffusion equation (FADE). This step connects the particle-scale memory effect with the field-scale Eulerian description. Since experimental observations of transient concentration evolution are often difficult to obtain, the proposed method focuses on cross-scale internal consistency rather than direct data fitting. The steady-state concentration profiles produced by the particle model are then compared with laboratory measurements to assess whether the long-term transport behavior is physically reasonable.

Building on the validated steady-state profiles, a fractional entropy formulation is used to describe the statistical structure of sediment concentration distributions. The entropy parameter is not an empirical fitting coefficient, rather, it is interpreted as a potential indicator reflecting the cumulative effects of memory-driven transport processes. By comparing the mean-square displacement (MSD) at the particle scale, the FADE parameters at the field scale, and the entropy-based description, this study demonstrates that entropy parameter may be related to anomalous transport characteristics associated with long-term particle memory.

Overall, this study presents a multiscale interpretation of anomalous sediment transport in which particle dynamics, continuum transport equations, and statistical descriptions are treated in a mutually consistent manner. The results suggest that entropy-based parameters may have the potential to serve as compact and physically interpretable indicators of anomalous transport intensity. This framework provides a structured approach for connecting transport dynamics across scales and for extracting physical insights from limited observable information.

Keywords:Anomalous diffusion;Memory-driven transport; Multiscale processes; Fractional dynamics; Particle-based modeling; Statistical characterization