of gentle beach curvature. The refraction coefficient, Kp, amd angle, ap, 
can be determined as functions of the deepwater wave characteristics H,, T, a 
(or ap) and the angle of the shoreline at breaking, dy,/dx. 
In the case of a groin perpendicular to the shore, at x > - », the deep- 
water wave angle, a,, with bottom contours is equal to the angle a of the 
wave with the ox-axis since the shoreline has the same direction as the ox-axis; 
at x = 0 (i.e., at the groin), the shoreline becomes parallel to the incident 
wave crest very rapidly. Therefore, a, = o and 
i 
(10) 
8X |x = 0 
Qo = -tan™ 
In the general case, for any value of x 
oy. 
Be =il § 11 
ao a + tan ARE ( ) 
The breaking wave characteristics of wave height, Hp, water depth dz, 
and the angle of breaking op, can be obtained from the deepwater wave charac- 
ieriisiGLes SHA ah, and a5.) a5) vse eiven by ‘equation (11)))an) texms) of a) ;and 
dy,/dx which takes into account the curvature of the shoreline. The following 
equations permit a determination of Hp, dp, and ap, provided the bottom contours 
are parallel along a wave ray (Le Mehaute, 1961), but could be curved along the 
shoreline (Fig. 5): 
PAR ALLEL 
CONTOURS 
7 
Figure 5. Effects of wave refractions 
on a curved beach. 
