SECT. 5] 



627 



The latter will approximately be the case with "internal" surges in a shallow 

 sea (like, e.g., the North Sea) bordering on the open ocean which, by its very 

 large extent and its great depths, keeps the sea-level along the boundary nearly 

 constant. (The terminology of "internal" and "external" surges was introduced 

 by Corkan, 1948, 1950.) The extent to which the boundary condition 



C = 



:i3) 



for such an open boundary is justified has been studied theoretically by Velt- 

 kamp (1954) and Weenink (1954) for the case of a rectangular shallow sea 

 bordering on an infinite ocean (see Fig. 9) and being in equilibrium with a wind 

 blowing over it. It appears from these studies that condition (13) is indeed a 

 good approximation to actual conditions, especially if the ocean is very deep. 



Fig. 9. Model sea having one wide opening (CD) and a narrow one (AB). 



Different conditions prevail in places where our sea area has a more or less 

 narrow opening (such as, for example, the Straits of Dover is for the North 

 Sea). If the hydraulic "resistance" of the opening is not so great and the sea on 

 the other side has sufficient capacity, the opening acts as a "leak" which has an 

 influence on the water levels in the sea region considered. Here we may find a 

 boundary condition in the following way (Weenink and Groen, 1958 ; Weenink, 

 1958). Let AB in Fig. 9 be such an opening. Then we may assume the total 

 transport through AB to be a linear function of ^ab, the sea-surface elevation 

 between A and B : 



Unds = Tab = k{Ub-^**), 



where Un is the volume transport in the outward direction normal to AB, ds is 

 an infinitesimal line element of AB, k: is a proportionality constant and ^** may 

 be interpreted as the sea-surface height that would be found immediately out- 

 side the opening if the opening were dammed. For the purpose of computing 



