612 GROEN AND GROVES [CHAP. 17 



hand, (i) surges in which the periods are mainly determined by the variation of 

 the atmospheric action involved (wind stress, j)ressure difference) ; and, on 

 the other hand, (ii) surges in which tlie periods are mainly determined by the 

 properties of the body of water that is affected, the role of the atmospheric 

 agent being in this case merely to "asj^irate" or to "excite". 



(i) The former will be the case if (1) the atmospheric action oscillates with a 

 very narrow period spectrum, or a line spectrum, the surge then being a simple 

 forced oscillation with prescribed period(s), or (2) the atmospheric action shows 

 a very slow variation, which means that its time scale Ta is very large in 

 comparison with a period Tb characteristic of the reacting system, the latter 

 being at every moment in quasi-equilibrium with the atmosphere. 



driving force 

 response 



Fig. 1. Idealized cases of time variation of atmospheric action (the time direction is from 

 left to right) and of resulting surges (damped oscillation). 



(ii) The other extreme will be realized if the atmospheric action shows a 

 variation in time which either (1) has the character of a random noise with a 

 very broad Fourier period spectrum, giving rise to a quasi-stationary sea- 

 surface oscillation with a period Tb that is characteristic of the body of water 

 involved, or (2) is aperiodic with a time scale Ta-^ Tb, such as is illustrated by 

 the examples shown in Fig. 1, the resulting effect being then a damped oscilla- 

 tion. 



The time scale, or period, Ta, characteristic of the atmospheric action, is 

 defined locally. If the atmospheric system that causes the surge is moving 

 across the sea area involved and if its life time is long enough, we may write 



Ta = AjCa, (1) 



Ca denoting the velocity of displacement of the system and A its horizontal 

 extent in the direction of the displacement. 



The period Tb is understood to be characteristic of the body of water involved 

 in so far as it is determined by its geometry (and, to some degree, by a factor 

 of energy dissipation in the water). If the horizontal extent of the body of water 



