A METHDD FOR DRAWING ORTHOGONALS SEAWARD FROM SHDRE 



by 

 Thorndike Saville, Jr, 



As a wave moves shoreward from deep water and approaches a shore 

 line obliquely-j that portion of the wave in shallower water moves more 

 slowly than the offshore portion, and the wave crest bends to conform more 

 nearly to the bottom contours. In analogy with the refraction of light, 

 this chaiige in direction of a wave as it moves through shallow water is 

 termed refraction, and the magnitude of this change, together with the 

 change in vrave height associated with it, is most conveniently represented 

 by a refraction diagram, which generally shows a set of orthogonals, or 

 lines which are everywhere perpendicular to the wave crests « 



The use of refraction diagrams to show the effect of hydrography 

 in the offshore area on wave heights and direction has by now become 

 practically mandatory in many coastal and harbor engineering problems o In 

 general, refraction conditions over a sizeable reach of shore front must 

 be considered, but in some cases it may be enough to consider the refraction 

 effect only at a point, or over a very small stretch of shore „ This is 

 particularly true in dealing with the design of structures where the location 

 of the structure is determined ty other conditions (such as a jetty at an 

 inlet). In such cases it would be much more expedient and time saving if 

 the orthogonals could be drawn seaward from the shore rather than landward 

 from deep water, as is usually done. Then only those orthogonals bracket- 

 ing the point of interest would have to be drawn, instead of having to 

 draw a large group of orthogonals to obtain by successive approximation 

 the few orthogonals actually; needed. Such a method would also have 

 application in determining the deep water direction of wave trains whose 

 breaker angle or direction in shallow water can be measured, 



Dunham has previously done some work along these lines, particularly 

 in the developnent of fan diagrams for Jetty design (1). Apparently the 

 drawing of orthogonals seaward from the shore line was accomplished by 

 using the scale developed by Johnson, O'Brien and Isaacs (2) for the 

 crestless method of drawing refraction diagrams, merely reversing the pro- 

 cedure used for bringing the orthogonal into shore from deep water. 

 However this scale gives correct results only for very small changes in 

 direction of the orthogonal and low values of •^'vfaK siiice the angle 

 measured between the wave crest and the contour on the way out from shore 

 is less than that (Cf) measured on the way into shore by the amount of 

 turning, (i.e. /:i(X ) (Figure 1). Use of this scale in drawing orthogonals 

 seaward from shore is therefore limited to cases where JtX is less than 

 about one degree, and AL/£^y, is less than about 0.1. In general a smaller 

 change in orthogonal direction than actually occurs is obtained from this 

 scale . 



