Abstract

Water flowing over sand in fluvial and marine settings often results in the formation of current ripples. Found in modern and ancient deposits on Earth and Mars, ripple stratification records flow directions and fluid properties that are crucial to interpreting sedimentary records. Despite decades of observations of current ripples, there is no universal scaling relation to predict their size or to distinguish them from dunes. Here we use dimensional analysis and a new data compilation to develop a scaling relation that collapses data for equilibrium wavelengths of ripples forming under unidirectional flows. Results show that ripples are larger with more viscous fluids, coarser grains, smaller bed shear stresses, and smaller specific gravity of sediment. The scaling relation also segregates ripples from dunes, highlighting a narrow regime of transitional bedforms that have morphologic properties and sediment transport conditions that overlap with both ripples and dunes. Our analysis shows that previous absolute size–based definitions of ripples and dunes only hold for certain conditions, such as water flows transporting siliciclastic grains on Earth. The new theory allows estimates of ripple sizes in foreign fluids and on other planets, including meter-scale ripples in methane flows on Titan or in viscous brines on Mars.

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