SECT. 3] 



BEACH AND NEARSHOKE PROCESSES 



533 



The transition from pebble material to sand material is associated both in 

 models and in nature with a considerable decrease in the general littoral slope. 

 Since the height to which the swash rises on a beach face cannot be appreciably 

 less than the wave height H, the width of the beach must be given approxi- 

 mately by H cot /3. For small slopes the beach width will increase very rapidly 

 with decrease in ^. Thus, whereas the width of the pebble or cobble beach 

 rarely exceeds the minimum possible wavelength, that of sand beaches may 

 exceed the wavelength of short, steep waves. Similarly, whereas the period of 

 up-surge and down-surge on the pebble beach rarely exceeds the wave period 

 either in models or in nature, the corresponding period on a sand beach is 

 relatively far larger. Both of these factors, wliich are inter-related, appear to 

 affect the manner in which the wave breaks, and in consequence the resulting 

 littoral profile. 



METRES 



15 



10 



BEACH SLOPE- ».^9° 



W, cm Tisec ^^^/h^ 

 12 1.3 21 



II 3.3 79 



VERTICAL EXAG 5X 



25 20 15 



DISTANCE-- FEET 



10 



+ 0.8 

 + 0.4 



tL 



LlI 



-0.4 "- 



S 



-0.8 X 



\- 



Q. 



-1.2 u 



< 

 -2.0 ^- 



- 2.4 



Fig. 8. Comparison of mature miodel beach profiles formed by long waves {La/H(i = 19), 

 and by short waves {L(i/H(i = 2\), of nearly constant height. The model beach con- 

 sisted of coarse sand with a median diameter of 0.56 mm ; in each case the beach was 

 given an initial slope of 1 : 15 (4'^) and then subjected to waves for a period of 10 h. 

 Waves were generated in water 3.0 ft deep, but tabulated parameters are those com- 

 puted for deep-water conditions. (After Corps of Engineers, 1947.) 



D. Wave Steepness i 



Fig. 8, reproduced from the Corps of Engineers (1947, pi. 4), shows the 

 mature profiles of tw^o coarse-sand model beaches. While the material (sand of 

 0.56 mm diameter), the wave height (11.3 cm), and the still water depth 

 (91.5 cm) were the same in both cases, the wavelengths alone were different. 

 The continuous line represents the profile formed by long waves with a wave- 

 length to wave-height ratio of 79, w^hile the broken line depicts the profile 

 formed by shorter and steeper waves, for which the ratio length to height was 

 22. The change from long to steep waves had the effect of removing material 



1 Ratio of wave height to wavelength. 



