Impulsively Generated Waves Propagating into Shallow Water 



Fig. 4. Wave breaking criteria 



(b) Decay of wave height after breaking is given by, 







where , 



(20) 



Hq , hj, = wave height and water depth at a point after breaking 

 H , h = wave height, water depth at breaking 



The expression is for two-dimensional waves. In the explosion- 

 generated wave case to account for geometric spreading the expres- 

 sion must be multiplied by the ratio oCy^/ot where a is obtained from 

 Eq. (12). " ° 



(c) The equation for wave stability after breaking is: 



CO n 



(f) =F?(°-«^-«-^of') 



(21) 



Stable 



The wave heights in Eqs. (17) - (21) reflect experimentally- 

 measured quantities; however the wave height information we have 

 at hand is computed from the linear theory of Eq. (12). Linear 

 theory is known to underpredict wave shoaling as the wave height 

 becomes a substantial fraction of the water depth. In addition, in 

 the final stages before breaking the wave front slows more rapidly 

 than the back. Associated with this developing wave slope asymnnetry 



253 



