H^ - H^ 





\ ^/ 



//. 



O). 



C + U 



N 



c„ 





\ 

 / 



f 1 1 





(11) 



where C =oj/k is the wave celerity. The second expression on the right-hand side of 

 Equation 1 1 for H2 is obtained by substituting o, =(02=(o^2^k2 U2. If Regions 1 

 and 2 are both located in shallow water. Equation 1 1 reduces to: 



^2 = 





^1 



1 



i. 





(12) 



Breaking Formulations 



There is little information on breaking criteria for wave breaking on a current. 

 Most nearshore breaking criteria neglect current and are based on relative water 

 depth, defined as the ratio of wave height to water depth, but existing criteria that 

 include wave steepness are good candidates for application on a current, e.g., 

 Miche's criterion (195 1) given by 



H = 0.142 L tanhW 



max 



(13) 



where H,^ is the Umiting regular wave height, X is wavelength, k is wave number, 

 and d is water depth. The strength of this relationship is that it reduces to a 

 steepness limit in deep water and a depth hmit in shallow water, thus incorporating 

 both limiting factors in a simple form. Battjes and Janssen (1978) apphed the 

 Miche criterion with the concept of energy dissipation in a bore (LeMehaute 1962) 

 for irregular waves in the following form 



D- -0.25 Q,f 



Ht 



(14) 



Chapter 4 Results 



17 



