Shallow Water Wave Transformation through External Factors 129 



propagation and in the height of the waves can be found graphically by 

 constructing a "refraction diagram", a term first used by O'Brien and 

 Mason (1940). 



A refraction diagram is one on which the position of wave crests at the 

 sea surface is shown by a series of lines. These are evenly spaced in deep 

 water — that is, in water of depth greater than half the wave length. Beyond 

 this depth the effect of bottom contours on any of the wave characteristics 

 is negligible. At shallower depths the relation between wave velocity and 

 water depth is known (see later reference), and a refraction diagram can 

 be constructed by advancing various points on a crest through distances 

 determined from any chosen time interval and the average depth. The 

 direction of advance is drawn normal to the crest. In Fig. 59 for example, 

 the chosen time interval is one wave period, and the distance A -A'. The 

 distance B -B' represents the advance of point B during the same time 

 interval, but for the average depth between B and B' . The lines A -A' and 

 B -B' are normal to the wave crests. By locating a set of points, A', B', C, ..., 

 the new crest can be found with sufficient accuracy by drawing a smooth 

 line through these points. Advancing one wave length at a time, the crests 

 may be carried into any depth of water desired, and the completed diagram 

 shows the continuous change in the direction of a wave advancing from 

 deep into shallow water. 



Description of a practical procedure for constructing refraction diagrams, 

 together with the necessary graphs and tables, can be found in the forecasting 

 manual (Written by Sverdrup and Munk and published by the Hydrographic 

 Office, 1944). The completed diagram can be interpreted in one of two ways: 



(1) As a series of lines representing the positions of a single wave crest 

 at various times as the crest advances towards shore. Crest interval is then 

 defined as the interval between these times. In Fig. 59 the crest interval equals 

 one wave period. 



(2) As a series of lines representing the position of certain wave crests 

 at a single instant ; a crest interval of one wave length means that every crest 

 is represented (Fig. 59), because the advance of any point on a crest during 

 one wave period equals one wave length by definition. A crest interval of 

 two wave lengths means that only every second wave crest is shown; a crest 

 interval of one-half wave length, that the position of every crest and trough 

 is shown. 



Wave height is defined as the vertical distance between crest and trough. 

 In order to evaluate the effect of refraction on wave height, a set of orthogonals, 

 that is, a family of lines which are everywhere perpendicular to the wave 

 crests, must be constructed. The lines A -A and B -B in Fig. 59 are or- 

 thogonals; they may be visualized as the wakes behind two surfboards which 

 are continuously oriented normal to the crest, that is, in the direction of 

 wave motion. Assuming that the wave energy is transmitted in the direction 



