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GRAPHICAL CONSTRUCTION OF WAVE REFRACTION DIAGRAMS 



BY 

 THE WAVE FRONT METHOD 



INTRODUCTION 



The height, period, and direction of waves in 

 deep water at an offshore point may be estimated, 

 either by direct measurement with suitable instru- 

 ments or directly from synoptic weather maps by 

 the forecasting method of Sverdrup and Munk.' 

 When waves move shoreward from deep water 

 and approach the shore line at an angle, the wave 

 crests are bent because the inshore portion of the 

 wave travels at a lower velocity than the portion 

 in deep water; consequently, the crests tend to 

 conform to the bottom contours. Figure 1 shows 

 the bending, or what is called "refraction," of 

 waves near a shore line. The results of refraction 

 are a change in wave height and in direction of 

 travel. The amount of these changes is best 

 estimated by use of a "refraction diagram." 

 Such a diagram might be prepared entirely from 

 aerial photographs, as was done in figure 2, but 

 generally they are constructed graphically. A 

 refraction diagram may be considered to be a map 

 showing the wave crests at a given time, or the suc- 

 cessive positions of a particular wave crest as it 

 moves shoreward. Only crests several wave lengths 

 apart are required to show the bending of the 

 waves and thereby permit the construction of a 

 set of lines which are everywhere perpendicular 

 to the wave crests (fig. 2). These lines are known 

 as "orthogonals", and the wave energy between 

 any two orthogonals is considered to remain con- 

 stant in estimating variations in wave height. 

 The power transmitted by a train of sinusoidal 

 waves is, 



Here, Cg is the velocity of transmission of the 

 energy, w is the weight of water per unit volume, 

 h is the length of crest (perpendicular to the local 



' Wind Waves and Swell, Principles in Forecasting, 

 Hydrographic Office, Misc. Pub. 11275. 



direction of travel) and H is the height from 

 trough to crest. Ocean waves are not exactly 

 sinusoidal, and their departure from this form 

 increases as they approach the condition of break- 

 ing, but this formula is sufficiently precise for 

 estimating wave heights and can be corrected by 

 empirical results in the vicinity of the line of 

 breakers. If no energy flows laterally along the 

 wave crest, then, in a steady state of wave motion 

 the same power should flow past all positions 

 between two orthogonals. Indicating the condi- 

 tions in deep water by the subscript zero, 



H 



"Vl- '-" 



A" 



The quantity -\/t is termed the refraction co- 

 efficient. It will be designated at Ka. The 

 — 1^ represents the effect of a change 



in depth on the wave height. It will be desig- 

 nated as D. The wave height in any depth of 

 water then may be written as. 



It is the purpose of this report to present 

 methods of determining Ka, the refraction co- 

 efficient. 



It should be noted that the values of both D 

 and Ka depend upon the depth and that they are 

 usually opposite in effect. Refraction commonly 

 tends to increase the length of the wave crest and 

 thus to reduce the height while D, representing 

 the effect of shoaling, tends to increase the height, 

 except in a relatively unimportant range of 

 depths where the waves first "feel the bottom." 

 For reference, values of D are presented in table 1 . 

 (For additional details, see plate I, Breakers and 

 Surf, H. O. No. 234, U. S. Navy, where it is 



