Interestingly, the use of the linear wave theory to evaluate the 

 value of the shoaling coefficient extends much beyond the formal 

 validity of this infinitesimal wave theory. Similarly, the value of 

 the shoaling coefficient given by the Stokesian wave theory extends 

 into the area where the cnoidal theory fits best. This is due to the 

 fact that, the shoaling coefficient being the ratio of wave height 

 H/Hq only, the increase in free-surface elevation under the crest is 

 partly balanced by the increase of free-surface elevation under the 

 wave trough. However, that the linear wave theory applies for the 

 shoaling coefficient does not mean that all wave characteristics 

 (wavelength, velocity components, pressure, acceleration) follow the 

 same principle; after the local wave height is obtained, all other 

 wave characteristics are determined by the appropriate theory. 



3. Comparison Between Theory and Experiment • 



A relatively large number of experiments have attempted to 

 verify shoaling laws; all have been conducted in laboratory wave flumes 

 with waves generated by wave paddle. Most of these experiments suffer 

 lack of accuracy because they were either done at too small a scale 

 and were subsequently subjected to significant scale effects such as 

 large viscous damping experiments (Iversen, 1951), or the wave paddle 

 generated not only monochromatic waves but harmonic components 

 (solitons) which introduced significant error and scattering 

 (Eagleson, 1956; Iwagaki, 1968). 



There is actually considerable controversy whether waves of 

 steady-state profile exist, as demonstrated by Dubreuil-Jacotin (1934). 

 Theorists Benjamin and Feir (1967) and experimentalist Galvin (1970) 

 postulate that the disintegration of finite amplitude monochromatic 

 wave occurs in deep water even on horizontal bottom. There are as many 

 theoreticians who assume that a steady-state profile does exist as there 

 are experimentalists who do not notice the "creations" of solitons. 



Use of a formulation developed by Mei and Le Mehaute (1966), 

 Peregrine (1967) , and Madsen and Mei (1969) indicates that for a 

 sufficiently abrupt change in water depth, both a solitary wave and a 

 cnoidal wave disintegrate into multiple crests. These results have 

 been obtained numerically and verified experimentally. However, over 

 a relatively gentle beach, the wave period remains constant between 

 deep water and shallow water and no disintegration takes place. Dis- 

 integration takes place when the wave arrives on a reef. It seems 

 natural to assume that the difference between these two observations 

 is due to the difference in bottom slope. Benjamin and Feir (1967) 

 show that waves are unstable if kd > 1.4; however, experiments by 

 Flick (1978) indicate that kd can be much larger without evidence of 

 wave disintegration or spectral smearing. 



It is commonly accepted that a monochromatic wave arriving on a 

 rapid change of depth (in diffraction zone) gives rise to at least a 

 doubling of crests. Such phenomenon is due to the nonlinear con- 

 vective effects. Iwagaki and Sagai (1971) also investigated the 



