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Reynolds-Froude scale modeling using hot-water flows to model cold-water flows was applied to the study of unidirectional-flow bed configurations in a large, thermally insulated laboratory flume. Three different water temperatures, ranging from 14 to 75 degrees C, provided three different scale ratios, from 1.1 to 2.3. Effective sand sizes, scaled to 10 degrees C water, were about 0.12 mm, 0.18 mm, and 0.28 mm. Relative to 10 degrees C water, use of hot water multiplied the effective flow depth and all flume dimensions by factors of up to 2.3, the flow velocity by factors of up to 1.5, and the water discharge by factors of up to 8. The effective dimensions of the flume, scaled to 10 degrees C water temperature, ranged up to over 26 m long and 2 m wide, with a flow depth of up to 0.5 m. In the coarser sand sizes (0.17-0.26 mm), three bed phases were observed: ripples, dunes, and upper-regime plane bed. Dunes tended to be two-dimensional (crests straight and continuous) at low flow velocities and three-dimensional (crests sinuous and discontinuous) at relatively high flow velocities, except that at flow velocities transitional between ripples and dunes the bed showed a complex intermingling of irregular larger dunelike bed forms and smaller irregular ripples. In the dune range, ripples were prominently superimposed at relatively low flow velocities but nearly absent at relatively high flow velocities.

Data from 39 flume studies that report equilibrium bed configuration as well as water temperature, flow depth, flow velocity, and sediment size are used to develop the best approximation to the relationships among bed phases (ripples, dunes, lower-regime plane bed, upper-regime plane bed, and antidunes) produced by flows of water over loose sediments. We use a three-axis graph with dimensionless measures of mean flow depth, mean flow velocity, and sediment size along the axes. The relationships are presented as a series of depth-velocity sections and velocity-size sections through the dimensionless diagram. Boundaries between stability fields of the bed phases were drawn as smooth surfaces that minimize misplacement of data points. A large subset of the data, for which reliable values of bed shear stress are reported, was used to represent the stability relationships of the bed phases in a graph of dimensionless boundary shear stress against dimensionless sediment size. The graph shows substantial overlapping of the fields for dunes, upper plane bed, and antidunes owing to the decrease in bed shear stress in the transition from dunes to plane bed with increasing flow velocity. The topology of bed-phase boundaries was guided by the relationships shown in the dimensionless depth-velocity-size diagram.