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 dunes) appears to lie between 80 130 grain diameters ( L = 80–130 D mm ). Starting with an 100 , subsequent bedform growth proceeds by amalgamation two successive bedforms, which results in a doubling each step. Geometric principles dictate that combined volume smaller lacks about 40% required for fully developed amalgamated bedform. The missing is gained excavation troughs, i.e., lowering base level. Where level prevented presence coarse-grained armor layer or hard ground pavement, larger remains sediment starved. In its simplest form, continuous response increases flow velocity, process being reversible decelerations. Bedform terminates when shear velocity u * ) at crest reaches mean settling w s sediment. At this point, bed material suspension, point can no longer be compensated trough excavation. shallow water, maximum size dictated water depth, whereas deep potentially grow their ultimate size. Evaluation data from settings suggests largest two-dimensional, terms (phi) approximated equations: ln max 13.72–4.03 phi H 9.95–3.47 sizes < ~ 0.2 (> 2.32 phi), representing height meters phi. For > (< 3.23 corresponding relationships are 6.215–0.69 3.18–0.56 notations as before, mm: 5 × 10 .