In general, the refraction problem is treated even less 
specifically for practical purposes. Given the deep water wave 
direction, amplitude and period of a pure sine wave, data are 
usually provided which give the angle the crest makes with the 
shore and the amplitude of the sine wave as observed at one point 
of special interest. For example, the data presented by Pierson 
(195la] for Long Branch apply only to one point, namely the point 
where the wave recorder used to be. It was at a depth of 21 feet, 
mean low water, offshore from latitude 40°18.2'. It is now at a 
depth of 30.5 feet, mean low water, offshore from latitude 40°18.2'. 
The slight change in location has negligible effects for this case 
since most of the refraction occurs in deeper water. 
In figure 32, consider the point B, in deep water just outside 
of the transition zone. At the point B, Xp and Yp are zero and the 
wave system will be referred to the Cartesian coordinate system in- 
dicated on the figure. If a pure sine wave of spectral frequency, 
Hy» were to exist in deep water and if it were traveling in the 
direction, ey” (measured with respect to o,* equal to zero coincident 
with the Xp axis), then the sea surface could be given by equation 
(12.23). The equation would hold everywhere in deep water. In the 
transition zone, equation (12.23) is not valid. 
In figure 32, consider the point C in the transition zone. At 
the point C, XR and Yp are zero. The XR axis is parallel to the 
Xp axis (and not necessarily coincidental). The depth at that point 
is H(xp,yp) = H = H(0,0) referred to this coordinate system. If the 
assumptions of wave refraction theory hold, then the bottom is nearly 
level at that point, The crests although slightly curved will have 
41 
