The limits to growth: how large can subaqueous, flow-transverse bedforms ultimately become?

Abstract

Based on field and experimental evidence, the average initial spacing (seed wavelength) of flow-transverse bedforms (ripples and dunes) appears to lie between 80 and 130 grain diameters (L = 80–130Dmm). Starting with an average initial spacing of L = 100Dmm, subsequent bedform growth proceeds by amalgamation of two successive bedforms, which results in a doubling of the spacing in each step. Geometric principles dictate that the combined volume of two smaller bedforms lacks about 40% of the volume required for a fully developed amalgamated bedform. The missing volume is gained by excavation of the troughs, i.e., by lowering the base level. Where base level lowering is prevented by the presence of a coarse-grained armor layer or hard ground pavement, the larger amalgamated bedform remains sediment starved. In its simplest form, bedform growth proceeds by continuous doubling of the spacing in response to increases in flow velocity, the process being reversible in response to flow decelerations. Bedform growth terminates when the shear velocity (u*) at the crest reaches the mean settling velocity (ws) of the sediment. At this point, 40% of the bed material is in suspension, at which point the missing volume can no longer be compensated by trough excavation. In shallow water, maximum bedform size is dictated by the water depth, whereas in deep water, bedforms can potentially grow to their ultimate size. Evaluation of bedform data from deep water settings suggests that the largest two-dimensional, flow-transverse bedforms in terms of grain size (phi) can be approximated by the equations: lnLmax = 13.72–4.03Dphi and lnHmax = 9.95–3.47Dphi for grain sizes < ~ 0.2 mm (> ~ 2.32 phi), with L and H representing bedform spacing and height in meters and D the grain size in phi. For grain sizes > ~ 0.2 mm (< ~ 3.23 phi), the corresponding relationships are lnLmax = 6.215–0.69 Dphi and lnHmax = 3.18–0.56Dphi, with notations as before, or in terms of grain diameters in mm: Lmax = 5 × 105Dmm.