Bedform spacing from defect dynamics

Spacing is a time-varying characteristic of bedform fields deriving from the behavior of defects (ends of crest lines) in the bedform pattern. In a model based on this hypothesis, crest line length is lost and spacing increases because bedform defects, which are smaller in height and faster migrating than surrounding bedform crest lines, merge with larger bedforms as defects migrate through bedform fields. Spacing in large bedform fields asymptotically increases with the logarithm of time as pairs of oppositely facing defects meet and annihilate. Spacing in small bedform fields, such as flumes, exponentially approaches a fixed value as defects are eliminated at the boundaries of the field. Model predictions are compatible with observed spacing of transverse bedforms, ripples formed under waves and linear dunes, calling into question the widespread assumption that bedform spacing approaches a steady-state value characteristic of fluid flow and sediment transport over two-dimensional bedforms.