SECT. 5] SURGES 637 



was 10 m/sec and 21 h if it was 20 m/sec. The maximum oscillation period of a 

 surge of the North Sea (in the length direction) is about 36 h. 



The above somewhat rough analysis of the local relation between C{t) and 

 ^o(0 niay be formally refined by means of a mathematical model which is 

 developed from equation (40) by introducing on its right-hand side terms 

 representing the driving forces, in such a way that in the stationary case one 

 obtains ^ = ^o : 



A simplification of this model, obtained by putting c = 0, was applied by 

 Weenink (1956) to the "twin" storm surges of 21-24 December, 1954, in the 

 North Sea, as recorded at the Hook of Holland. He found for that case (putting 

 c = 0) the values a = 0.06h-i and 6 = 0.20 h"!. According to (8) this would 

 correspond to a period of free oscillation To = 33 h (without damping it would 

 be 31 h). The resonance period Tr, i.e. the period which a harmonic oscillation 

 of ^0 must have in order to give a forced oscillation of ^ with maximum ampli- 

 tude, is somewhat different from To, 



Tr = 277/v'(62-2a2). 



With the above values of a and b we have Tr=34.5h. The time interval 

 between the two successive storm-surges was 36 h in that case, so that there 

 was nearly complete resonance, a fact which also appears from the large time 

 lag (6h). While the equilibrium effect oscillated with an amplitude of 1.5 m, 

 the first actual maximum was 0.3 m higher and the second one 0.55 m higher 

 than the corresponding equilibrium maximum. If a third storm of equal 

 strength had followed with the same time interval, the third maximum would 

 hardly have been higher. This is a consequence of the fact that damping was 

 strong during this prolonged storm period. (See Fig. 8.) 



(n ) Air-pressure surges 



The effect of a changing atmospheric pressure disturbance has long ago 

 been studied by Proudman (1929, 1953) and more recently, among others, by 

 Harris (1957a) and Platzman (1958). The theory of this effect shows a complete 

 formal analogy with the theory of forced tides, as is seen from equations (3) 

 and (4), where p~^ Vpo and Vg play similar roles. 



Proudman showed that the effect of an atmospheric disturbance travelling 

 with velocity V over a semi-infinite canal-shaped body of water of depth h 

 (undisturbed), if friction is neglected, is inversely proportional to 1 — V^/gh. 

 So, resonant coupling will occur when V = s/igh). Such resonance has been 

 observed, e.g., on 26 June, 1954, in Lake Michigan. This case has been described 

 by Ewing et al. (1954), Harris {loc. cit.) and Platzman {loc. cit.). 



Of course, an atmospheric pressure effect will in general be accompanied by 

 a wind effect and much of what has been said about wind surges applies also 

 to air-pressure effects. In most cases the latter will be outweighed by the wind 

 effects. 



