Abstract

Use of depth and mean velocity to characterize bed configurations in uniform open-channel flow over a loose sediment bed leads to a three-dimensional diagram, with dimensionless measures of depth, mean velocity, and sediment size (or these three variables themselves) as coordinates, with the property of one-to-one correspondence between possible bed configurations and points in the diagram, thus eliminating overlapping of fields in diagrams involving bed shear stress. The diagram is most readily visualized by means of depth-velocity sections for a series of sediment sizes. Depth-velocity diagrams plotted from U. S. Geological Survey flume data for five sediment sizes ranging from fine sand to very coarse sand show contiguous but nonoverlapping fields for ripples, dunes, transition, and flat bed (is the finer sands) and lower flat bed, dunes, transition, and upper flat bed (in the coarser sands), with increasing mean velocity; field boundaries are almost parallel to the depth axis or slightly inclined. Each of these fields is truncated by a field for standing waves and antidunes at smaller depth or higher velocity. A size-velocity section for a depth of 0.2 m constructed from the depth-velocity sections shows more clearly the relations among the bed-configuration fields with varying sediment size. Several lines of evidence indicate that the dune field, which lies between the fields for ripples and flat bed in the fine to medium sand range, wedges out with decreasing sediment size at about 0.08 mm; in finer sediments, ripples pass directly into a flat bed. The relations between the ripple field for finer sands and the lower flat-bed field for coarser sands is unclear. If the densities of fluid and sediment are varied, then there is a different depth-velocity-size diagram for each ratio of sediment density to fluid density. The wide gap in density ratio between the cases of sand in water and sand in air on Earth might be bridged by experiments at intermediate density ratios.

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