Constraining the Distribution of 3D Fractal Structures in Mud Flocs

Mud builds coastal landscapes and governs the long-term evolution of river deltas, floodplains, and estuaries, yet predicting its transport remains difficult because mud aggregates into flocs with complex, fractal structures that deviate from simple particle behavior. The three-dimensional (3D) fractal dimension of these flocs sets their settling and sediment transport characteristics, but reliably determining this parameter across diverse environments is a persistent challenge. Conventional aggregation of floc data often obscures real structural diversity and can yield misleading fractal dimensions due to Simpson’s Paradox. This study tests the hypothesis that stratifying settling data by image-derived two-dimensional (2D) fractal dimension enables more accurate inference of the hydrodynamically relevant 3D fractal dimension. Controlled experiments with freshwater flocs, formed under varied shear and particulate organic matter (POM) conditions, were conducted using in-situ imaging, PIV-corrected tracking, and box-counting analysis to resolve structural differences. Results demonstrate that aggregation overestimates the 3D fractal dimension, while stratification reveals clear trends: the inferred 3D fractal dimension increases with shear stress and decreases with particulate organic matter content. These findings provide a basis for more realistic floc modeling and improve predictions of fine sediment transport.