A Fractal Approach for Characterizing Microroughness in Gravel Streams

Discrete cluster microforms, or simply clusters, in gravel streams result from organization of particles found in the surface layer of the gravel bed into disconnected patches. Clusters are the outcome of feedback interaction between flow, sediment and stream planform geometry. The complexity of this interaction results in several different cluster shapes, i.e. line, rhomboid and triangular. The objective of this research is to provide a quantitative characterization of cluster shape. To achieve this, we employed a novel method based on fractal theory and used for the shape description of clusters. Our novel method utilized the cell-counting method for the estimation of the areal fractal dimension, for two major datasets, namely fabricated clusters with well-defined shapes, and clusters developed in the laboratory. The principal finding of this research is that the proposed method successfully characterized cluster shape in quantitative terms. Specifically, it was shown that the new approach could identify clusters of different shapes 84% of the time, under different arrangements. This finding is of great importance for bed pattern recognition studies of stream reaches with superimposed roughness elements such as clusters. The findings of the current work could also assist numerical modellers in the development of more representative models of flows over roughness features such as clusters and in the interpretation of results from such models.