Does turbulence show fractal structure within a dynamic undercut of an alluvial riverbank?

Abstract

Characterization of the processes associated with riverbank erosion is crucial for predicting bankline retreatment and river-form migration. The present study examined the scaling or fractal structure of the turbulence characteristics within a progressing undercut of an eroding riverbank. The study employed different methods to examine the existence of scale-invariance in the turbulence data within the undercut to characterize the coupled dynamics of the undercut depth increment and the turbulence velocity fluctuations. The methods used included box counting dimension, probability distribution function, power spectral density, continuous wavelet transform, and Shannon entropy. The results from the box-counting method showed that the fractal dimensions of the turbulent flow depend on the distribution of the eddy scales of the turbulent flow field. This could be further related to the interactions with the rough boundary of the sediment bank. A shift in the eddy scales was observed as the erosion progressed for the different undercut depths, demonstrating the evidence of fractality at the intermediate scales representing the inertial sub-range. The fractal dimension calculated using the power spectral density showed similar results as to that obtained from the box-counting method. Furthermore, the results portrayed that the turbulence structures exhibited greater organisation within the undercut region when compared to that in the near-bank surface region. The results also helped characterize the co-evolution of the bank undercut and the scales of turbulent velocity fluctuations.