Chapter 12. WAVE REFRACTION IN THE TRANSITION ZONE 
Introduction 
The assumption that the oceans are infinitely deep have proved 
very useful so far in the study of ocean waves. For all practical 
purposes, the errors involved are not important. Sooner or later, 
somewhere, the disturbance is dissipated by the breaking of the waves 
on a coastline. Waves leave the deep parts of the oceans and travel 
finally to the shallow waters bordering a coast of an island or a 
continent. In the shallower waters, if the depth is constant over a 
relatively large area, the wave crest speed of a purely sinusoidal wave 
is given by equation (12.1). But wave refraction complicates the 
problem, and it is necessary to treat the wave crest speed as if it 
were a slowly varying function of position. There are varying degrees 
of accuracy with which the problem of wave motion over an area where 
the depth is less than, say, one half the wave length of the lowest 
important spectral component, can be treated. These methods will 
be discussed in this chapter. 
As the waves advance into an area where the effect of depth is 
important, a large area can be found such that the results of the 
previous chapters can be extended to explain the observed patterns 
and aerial photographs. Later, as the waves near the breaker zone, 
a transformation often appears to occur which substantiates some 
of the results of Munk [1949] on Solitary Wave Theory. Finally, the 
waves peak up and break. 
The breaking wave is a phenomenon of the non-linearity of the 
original equations of motion. All methods of wave analysis and wave 
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