NOTES ON THE FORMATION CF BEACH RIDGES 



by 



Rudolph P. Savage 



Research Division, Beach Erosion Board 



In laboratory experiments involving wave action on sand beaches 

 the beach ridges formed almost always have a characteristic shape. 

 This shape, shewn as a solid line in Figure 1, is created from the 

 original slope (shown) by the waves. One explanation of this shape 

 may be obtained by considering the relationship between relative 

 wave run-up (R/H) and beach slope (Figure 2) previously reported 

 (1,2). As shown in Figure 2, for any constant deep water wave 

 steepness and wave height, the relationship between wave run-up and 

 beach slope assumes a characteristic curve with the run-up increasing 

 as the slope steepens, up to a maximum value, then decreasing somewhat. 



If it is assumed that a beach ridge is created by a deep water 

 wave of constant height and steepness, the mechanics of beach ridge 

 formation might then be explained as follows: When the first waves 

 run up the original, say 1 on 20, slope, the maximum run-up is to the 

 point marked by R20 (Figure 1). As the waves surge up and down the 

 slope, a small deposit of sand is left by each wave, thus creating a 

 somewhat steeper slope. As the slope steepens, the run-up increases 

 (depositing sand to successively higher elevations) until at the time 

 the foreshore slope has steepened to 1 on 10, the run-up would be to 

 the point marked Rj^q in Figure 1. This process is continued until 

 the slope achieves a steepness which is limited by the size of the 

 sand and the characteristics of the waves creating the beach ridge. 



In Figure 1, it was assumed that all the slopes created by the 

 sand deposits would pivot around point A. It is not necessary that 

 this happen, and the slopes could pivot around some other point or 

 different points. Point A' and the dotted line for the 1 on 10 

 slope are shown on Figure 1 to give some idea of the effect that a 

 variable pivot point could have on the shape of the beach ridge. It 

 appears that as long as point A does not fluctuate too widely the 

 characteristic shape of the beach ridge would be essentially the 

 same. 



It should be noted from Figure 2 that if the foreshore of the 

 beach ridge becomes steeper than 1 on 5 for a wave with a deep water 

 steepness of 0.005, the run-up then begins to decrease. For waves 

 with steepnesses of 0,40, the foreshore slope must become steeper 

 than approximately 1 on 2 before the wave run-up begins to decrease. 

 In any event , the maximum height to which a beach ridge caui be built 

 would be a function of the maximum run-up for the particular wave 

 steepness under consideration. Under conditions where the slope 

 finally achieved by the foreshore of the beach ridge does not reach 

 the slope of maximum run-up given in Figure 2, the maximum height of 



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