A a is the cross-sectional area of flow through the entrance channel at 

 any point X between the seaward end at X s and the harbor end X^ 

 (A e , therefore, being a function of X), Afo a the cross-sectional area 

 at the bay end, A sc the cross-sectional area at the sea end, h s the 

 height of the sea level above the arbitrary fixed datum, and F defined 

 as the total bottom friction in the entrance channel. A sample compu- 

 tation for a tsunami entering a bay is given in Seelig, Harris, and 

 Herchenroder (1977) (Fig. 47). It can be seen that the peak water levels 

 in the bay occur slightly after the peak water levels just seaward from 

 the entrance channel. Also, the peak water levels were slightly lower 

 in this case. 



0.75 

 0.50 

 0.25 



I ° 



'3 



" -0.25 

 -0.50 h 

 -0.75 



Inlet length = 1 22 m 

 Inlet depth = 7.3 m 

 Inlet width =24 m 

 Bay area=4.6xl0 5 m 2 



Tsunami at bay entrance 



Water level in bay 



0.5 



1 .0 1 .5 



Time (hr) 



2.0 



2.5 



Figure 47. Tsunami water levels in a bay (tide excluded) 



(after Seelig, Harris, and Herchenroder, 1977). 



Miles (1971) found that he could transform his equations for wave- 

 induced oscillations in a harbor to an integral equation equivalent to 

 the equation formulated by Lee (1969, 1971). Lee expresses the governing 

 equations for wave oscillations in an arbitrary-shaped harbor as 



and 



d 2 Z 



dZ 2 



K Z Z 



(304) 



9 2 f(x,y) , 3 2 f(x,y) 



3x' 



3y< 



+ k 2 f(x,y) = 



(305) 



144 



