636 GROEN AND GROVES [CHAP. 17 



"perturbation term", C^^'>{t), which, of course, depends on the development in 

 time of the whole wind field, but which in many cases is chiefly determined 

 already by the development of ^o(0 ^^ the place under consideration. Elaborate 

 studies by Schalkwijk (1947) and Weenink (1956) and a routine practice of 

 forecasting sea-level heights along the Netherlands coast have indeed shown 

 this to be so, practically. It was found that a fair approximation of ^^^>(0 is 

 given by ^(i)(^)~ ^o{t— §) — ^o{i), so that one may write 



ao = ^o(^-s)+^<2)(^), 



where 8 is a time lag and ^<'-)(0 is a secondary correction term. At the Hook of 

 Holland, for example, the time lag for the North Sea wind effect is, according 

 to Schalkwijk {loc. cit.), 2 to 3 hours, on an average (see also Haurwitz, 1951, 

 who studied this effect theoretically). One may refine the use of time lags by 

 writing t,o{t) as the sum of contributions from different sub-areas of the sea and 

 using different time lags for the different sub -areas. 



Fig. 10. Schematical example of the difference between equilibrium wind effect (dashed 

 line) and actual wind effect, as functions of time. 



Physically, this time lag is a complex phenomenon. In places where the 

 Coriolis force has a negative effect when the water is rising and a positive effect 

 when the water is falling, as on the right-hand side of Fig. 9 (in the case of a 

 longitudinal surge), it adds to the time lag. In places, where the opposite occurs, 

 it diminishes the time lag. 



The secondary effect ^<2)(f) is mainly an oscillatory after-effect, following a 

 rise or fall of the equilibrium effect. It results mostly in "overshooting" and 

 "undershooting" of maxima and minima, as is illustrated by Fig. 10, which 

 gives an illustration of both the time lag and the secondary effect C^^'>{t), the 

 dashed line representing ^o(0 ^^^ ^he full line ^t). The amount of overshooting 

 or undershooting depends upon the preceding rate of rising or falling of the 

 equilibrium effect ^o and upon the development of ^o following the moment of 

 its maximum or minimum. In the case of a very steep rise of ^o immediately 

 followed by a steep fall, the "overshooting" of the maximum may even be 

 negative, i.e. the equilibrium maximum is not attained in that case. 



A free after-oscillation (such as is seen on the right-hand side in Fig. 10) has 

 a damping rate depending on the degree of turbulence in the sea, which in its 

 turn depends on the tidal currents and on the wind. For the North Sea, for 

 instance, Schalkwijk {loc. cit.) found the time needed for the amplitude (at 

 the Hook of Holland) to become halved to be 34 h if the mean wind velocity 



