Spectral behavior of gravel dunes

• Different spectral behavior exist between gravel and sand dunes
• A schematic spectrum of a gravel dune surface is proposed
• Kinetic and geometrical explanations for the spectral behavior are explored
• The special spectral behavior associate to the development of gravel sheets

Spectral behavior of gravel dunes formed under different flow discharges is analyzed with an attempt to verify the ‘− 3’ spectral law that has been confirmed extensively for sand dunes. A schematic spectrum of gravel dunes is proposed based on the spectral analysis as well as results from the literature. The results of spectral analysis show a significant deviation from the ‘− 3’ spectral law for gravel dunes, and the magnitude of deviation correlates with flow discharge. Possible explanations for the deviation from the ‘− 3’ spectral law, being associated with kinetic and geometrical characteristics, have been explored. To investigate the kinetic characteristics of gravel dunes, a wavelet-based method that calculates the celerity of dunes based on a pair of elevational time series is quantitatively tested. Our results suggest that (1) the kinetic explanation based on the relationship between dune celerity and dune length cannot fully explain the spectral behavior of gravel dunes; (2) the geometrical explanation based on the self-similarity hypothesis is confirmed by the relationship between dune length and dune height; and (3) the development of gravel sheets accounts for the differences in kinetic and geometrical characteristics between gravel dunes and sand dunes.