Longitudinal streaks

A commonly observed bedform in wide erodible-bed channels consists of rows of streaks or stripes parallel to the flow. These stripes can be manifested in terms of transverse variation of bed elevation, characteristic grain size (and thus roughness) or both. The former case is manifested most strongly in sediment with a nearly uniform size distribution and the latter most strongly in sediment with substantial heterogeneity in size. The amplitude of stripes is rarely larger than one or two grain diameters, and the transverse spacing is invariably of the order of the flow depth. They are closely linked to a pattern of paired cells of secondary flow in the flow cross-section. An existing theory of streak formation for the case of uniform sediment relies on a second-order turbulence closure which explicitly links the streamwise flow to transverse variations in bed elevation. The theory successfully predicts the formation of streaks, but only at rather high values of the Shields stress, i.e. rather strong sediment transport. Streaks are commonly observed, however, at Shields stresses as low as only slightly above the threshold of motion. In the present analysis the previous flow model is adapted to the case of transverse variation of roughness as well as elevation, and the constraint of uniform sediment is removed. The theory indicates that allowance for even slight heterogeneity of bed sediment results in the formation of streaks at any Shields stress above the threshold of motion. The resulting streaks are hybrid in the sense that they show transverse variation in both elevation and roughness. The model thus provides a general theory of streak formation.