436 



Walter Hansen 



solution in final analytical form. This is true also if — as is assumed here — there is 

 no mass transport perpendicular to the coast. Likewise the transport of water masses 

 across the northern Umit of the basin has been assumed to be zero. The problem 

 therefore has to be treated numerically. For this purpose a system of differences 

 equations was derived from hydrodynamical differential equations. These make it 

 possible to determine the elevation of sea level due to wind and the components of 

 the transport of the water masses at the points of intersection of a grid spread over 

 the North Sea. Details of this method are given elsewhere (Hansen, 1954). 



The grid used has been inserted on Fig. 1 . The wind field, used as a basis, has the 

 same wind direction throughout, parallel to the longer side of the basin. It is assumed 

 that the velocity of the wind is described as a sine function of the time co-ordinate 

 having for all points on the grid the same amplitude and phase. In the numerical 

 calculation, carried out for the values of to tt, related to a time interval of 12 hours, 

 the amplitude of the wind velocity has been chosen as 20 m/sec. 



WIND DIRECTION 



Fig. 2. Maximal elevation of a storm 

 surge in the North Sea based on theory 

 for a rectangular basin of variable depth 



For the tangential stress which the wind exerts on the surface of the sea, the value 

 in SvERDRUP, Johnson and Fleming (1942) of 3-2 x 10"^ x W^ was used, where 

 W(m/sec) stands for the velocity of the wind. 



The friction in the water is directly proportional to the current velocity or to the 

 gradient of the surface of the sea. 



The accessory value of the friction depends not only on the depth of the water 

 but also on the maximum velocity. For a water depth of 50 m and a velocity of 1 

 m/sec this has a value of 0-48 X 10"*. 



The numerical solution is found by applying the method of differences which has 

 been described in the paper mentioned above. 



In Fig. 2, the calculated fines of equal maximum elevation has been inserted. 

 While in the northern part of the basin a trifling fall of water level can be observed, 

 the elevation increases generally towards the south. The higher values in the western 

 parts of the basin are noteworthy, being apparently a result of the Coriofis force as 



