where the line integral f s is taken across the harbor entrance, 

 measured along the coastline (across the harbor entrance) , and x 

 measured normal to the coastline. 



y is 

 is 



Lee (1969) expressed equations (307) and (309) in matrix form and 

 solved them numerically. Figure 48 is an example of his experimental 

 results for a small laboratory model of an arbitrary-shaped harbor. 



Arbitrary -shaped 

 harbor theory 



Figure 48. Response curve at point C of the Long Beach harbor 

 model (from Lee, 1969) . 



Chen and Mei (1974) have developed a finite-element numerical model 

 which can be used to study water level oscillations in a harbor. Houston 

 (1976, 1977) applied Chen and Mei's model to studies of Los Angeles and 

 Long Beach harbors . 



VII. TSUNAMI RUNUP AND INTERACTION WITH STRUCTURES 



The arrival of a tsunami at a shoreline may cause an increase in water 

 level as much as 30 meters or greater in an extreme case. Increases of 

 10 meters (32.8 feet) are not uncommon. The large increase in water 

 level, combined with the surge of the tsunami, can impose powerful forces 

 on shore protection structures and on structures located near the shore- 

 line. Structures may be seriously damaged or destroyed by the tsunami. 

 Damage may be caused by strong currents produced by waves overtopping the 

 structures, by the direct force of the surge produced by a wave, by the 



146 



