Miche (1951) developed breaking criteria for smooth uniform slopes 

 extending to deep water. All waves incident to the slope would then be 

 considered deepwater waves. His condition for breaking waves is 



Ho sin 2 /2F- it , ,. . ,„, 



/ — for 6 < — (radians) . (4) 



gT z " 2^ \tt 4 



Miche's equation was derived to indicate the wave steepness at which 

 a wave would begin to break on a particular slope. This incipient 

 breaking was defined to occur when the reflection coefficient 

 Qireflected/tkncident) be came less than unity. This definition 

 assumes that nonbreaking waves have perfect reflection. 



For a given slope, however, there is a range of wave steepnesses 

 between incipient breaking and complete breaking. Incipient breaking 

 is the point at which the wave exhibits the first signs of instability, 

 such as slight spilling at the crest. Complete breaking would apply to 

 a wave which has become a plunging breaker or a turbulent spilling 

 breaker in approaching or moving onto a structure or uniform beach slope, 



Iribarren Cavanilles and Nogales y Olano (1949) (as referenced in 

 Hunt, 1959) gave a breaking criterion that indicates incident waves 

 meeting the following condition will break. 



-S- > 0.031 tan 2 6 . (5) 



gT 2 



Hunt noted that equation (5) gave a wave steepness value, H/gT 2 , inter- 

 mediate between complete reflection and complete breaking. He listed 

 the experimental values of Iribarren Cavanilles and Nogales y Olano, 

 but water depths were not included in the data. Nevertheless, both 

 Iribarren Cavanilles and Nogales y Olano (1950) and Hunt (1959) applied 

 equation (5) to slopes fronted by a finite depth. In such cases, depth 

 effects both on incident waves and on the breaking criteria would be 

 expected. Shallow-water and transitional-water waves (defined in 

 Table 1) would be expected to break at steepness values different from 

 deepwater waves . 



Available runup data have been obtained for predominantly nondeep- 

 water conditions, where relative depth is a factor in the wave's inter- 

 action with a slope. For a given relative depth, d s /gT 2 , relative 

 runup, R/H L? , increases with increasing wave steepness, H^/gT 2 , (for 

 a sufficiently low steepness) until reaching a maximum; R/HJ, values 

 then decrease with even larger values of H^/gT 2 . The wave steepness 

 corresponding to maximum relative runup is taken to be the point of in- 

 cipient breaking, or the largest wave steepness for total reflection. 

 Runup data show that maximum relative runup for dg/gT 2 > 0.0793 (i.e., 

 deep water) occurs at a wave steepness approximately the same as 



