Field and laboratory studies of ripples and dunes formed in sand by unidirectional water currents show for coarse and very fine sand that the ripple index is related to median particle size and to flow intensity as measured by a dimensionless shear stress parameter. However, for medium-grained sand (0.25-0.50 mm.)

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the ripple index is approximately constant and is independent of flow intensity. For medium-grained sand statistical properties of the ripples and dunes other than the ripple index are required to correlate the characteristics of the bed configurations with flow parameters.

Two methods of analysis for medium sand have been developed. In the first, spectral analyses of profiles of the channel bed lead to a linear second-order Markov model which describes the essential statistical properties of the dunes. All the parameters of the model are simple linear functions of the water discharge per unit width of channel. One of the parameters, the standard deviation of the bed elevation about the mean, shows excellent correlation (correlation coefficient of 0.99) with unit water discharge for flows ranging from 0.7 to 10 cfs. per foot of width and for average dune lengths from 2-25 feet.

The second method of analysis consists of defining distributions of dune lengths, amplitudes, ripple indices, and angles of downstream faces, and relating the moments of these distributions to flow characteristics. All the distributions are skewed, and the skewness correlates roughly with flow intensity. This analysis gives useful indications of the variations in the geometric properties of ripples and dunes, but it is time-consuming and requires extensive data. Moreover, the parameters describing the ripples and dunes show only a crude relation to flow characteristics. Of the two methods, the spectral analysis appears to be more useful.

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