626 GROEN AND GROVES [CHAP. 17 



It has the dimension of a velocity and may, e.g., be of the order of 0.2 cm/sec 

 (southern North Sea). 



B. Surges in Partly Enclosed Sea Areas of Restricted Extent 



This section deals with the type of surges occurring in an at least partly 

 enclosed sea region (or a lake) and affecting it more or less as a whole, according 

 to the distinction made in section 1-C of this Chapter. The latter condition 

 means that the sea area is not large in comparison with the horizontal dimen- 

 sions of the disturbing atmospheric system. Consequently, this condition is 

 different for tropical cyclones and extratropical storm depressions. 



a. Boundary conditions 



There are two sorts of boundaries here : closed boundaries, formed by coasts, 

 and open boundaries, where the sea region considered meets a different sea 

 region or the open ocean. 



Along a closed boundary we have the condition 



Un = 0, (11) 



where Un is the volume transport component normal to the boundary. This 

 condition applies to the two-dimensional treatment developed in section 3-A. 



A difficulty arises in connection with the depth going to zero at the shore-line, 

 since in the linearized theory infinities would show up there, unless the coast 

 were a vertical wall. Even the non-linear two-dimensional equations (3) 

 and (4) on page 622 offer no acceptable solution for the wedge-shaped strip of 

 water in the immediate vicinity of the shore line, e.g. in the simple case of a 

 stationary wind blowing at right angles with the coast. This difficulty has been 

 briefly discussed by Weenink (1958, p. 29), who showed that we make no 

 serious error if we introduce a vertical wall instead of the wedge-shaped strip of 

 water. An adequate theory of what happens in the immediate vicinity of the 

 shore-line will have to use the three-dimensional equations of motion and to 

 take the circulation in a vertical plane and wave action into account. For the 

 present treatment we shall confine ourselves to the two-dimensional theory and 

 shall, therefore, assume vertical walls as coasts. 



Along an open boundary, across which free transport of water can take place, 

 C or Un, or a quantitative relation between these quantities, must be given in 

 order to make the problem accessible to mathematical solution for the sea 

 area under consideration without further regard to adjacent sea areas outside 

 the boundary. 



The surface height disturbance ^ may be given, along the open boundary, 

 as a function of place on the boundary, s, and time, t, 



^=^Us,t), (12) 



giving rise to a so-called "external" surge propagating into our sea region (in 

 the same way as oceanic tides affect marginal seas and bays), or as constant. 



