The rate of littoral transport of sand induced by wave action on a straight beach inclined to the direction of the wave crest was studied in a model and related to wave characteristics. fixp* 3^m ental equipment--In a model basin approximately 66 ft by 122 ft in plan and two feet in depth, a wave machine and a model beach were arranged as shown in Figure 1. The wave machine was of the flap type in which the period of the waves could be varied by changing the speed of the driving motor, and the wave energy could be changed by adjusting the throw on the crank arms connected to the wave flaps. The wave height and wave length were determined by the period and energy settings. 565 WATERS, C H., Equilibrium slopes of sea beaches,
The distribution of wave steepness (H/T ) for fully developed sea is obtained from Bretschneider's joint distribution of wave height and wave period. This steepness distribution is used with standard wave runup curves to develop a frequency curve of wave run-up. Use of this run-up distribution curve will permit more accurate estimation of the variability in wave run-up for design cases, and particularly the percent of time in which run-ups will exceed that predicted for the significant wave. The distribution may also be used with normal overtopping procedures to determine more accurate estimates of overtopping quantities. Wave run-up may be defined as the vertical height above mean water level to which water from a breaking wave will rise on a structure face. Accurate design data on the height of wave run-up is needed for determination of design crest elevations of protective structures subject to wave action such as seawalls, beach fills, surge barriers, and dams. Such structures are normally designed to prevent wave overtopping with consequent flooding on the landward side and, if of an earth type, possible failure by rearface erosion. Because of the importance of wave run-up elevations in determining structure heights and freeboards, a great deal of work has been done in the past six years in an attempt to relate wave run-up to incident wave characteristics, and slope or structure characteristics. Compilations based largely on laboratory experimental work have been made and have fe-?* suited in curves similar to those shown in Figure 1 which is reprinted from the U. S. Beach Erosion Board Technical Report No. 4. Such curves most frequently have related the dimensionless ratio of relative run-up (R/H ) to incident wave steepness in deep water (H /T ), as a function of structure type or slope. (H is the equivalent deep water wave height.) The curves shown in Figure 1 are of this type, and pertain to structures having a depth of water greater than three wave heights at the toe of the structure; this depth limitation in effect means that the wave breaks directly on the structure. The curves shown in Figure 1 are a portion of a set of five separate figures, covering different structure depths (d/H ). All are published in Beach Erosion Board Technical Report Number 4. These curves were derived primarily from small scale laboratory tests. Further laboratory tests with much larger waves (heights two to five feet) have shown that a scale effect exists for some conditions.
Prior to the time the Committee on Runoff of the Boston Society of Civil Engineers published their report (Report of the Committee on Runoff, J. Bos. Soc. C. E., v. 9, No. 8, 1922), duration‐curves of stream‐flow had been prepared almost universally by plotting the runoff in cubic feet or in cubic feet per second per square mile as ordinates against the cumulative percentage of time as abscissae. [Note: Throughout this paper the basic unit of stream‐flow is defined as rate of discharge in cubic feet per second.] This report showed that if the ordinates were expressed as ratios to the mean flow, the duration‐curves for different streams in New England would be surprisingly similar, regardless of any differences in the size and character of the drainage‐basin, or in the total flow. This procedure, originally proposed by Hazen (Allen Hazen, Discussion of Power‐estimates from stream‐flow and rainfall‐data, by Dana Wood, J. Bos. Soc. C. E., v. 3, No. 3, 299–303, 1916), is confirmed by Barrows (H. K. Barrows, Water power engineering, p. 128, 1927), who maintains “…that for the rivers of the east and south the flow, as a per cent of the mean, could be expressed, for the dryer 80 per cent of the time, by the formula, log Q = (2.40 ‐ 0.011 T), where Q is discharge as a per cent of the mean and T is per cent of time.”
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