628 GROEN AND GROVES [CHAP. 17 



sea-surface heights in the case of a wind surge it is practicable not to use the 

 actual elevation ^ab for the boundary condition but the elevation ^*ab which 

 would result on the inner side of the opening if it were dammed : 



nB = A(^*AB-^**). (14) 



For the Straits of Dover, as an example, the factor A has been estimated at 

 7 X 105 m2/sec (Weenink and Groen, loc. cit.). 



b. Quasi-equilibrium theory 



In many cases the response of the sea to the wind stress or the pressure 

 gradient does not differ much from the equilibrium response that would result 

 if the atmospheric conditions were stationary. In other words, in those cases 

 the theoretical equilibrium state of the sea corresponding to the prevailing 

 atmospheric conditions is a good first approximation to the actual state. The 

 smaller the body of water affected and the slower the variation of atmospheric 

 conditions, the better this approximation. Indeed, various methods of fore- 

 casting wind surges in certain sea regions use this approximation successfully, 

 applying only a time shift of a few hours to it, which accounts for the time lag 

 that is found between the actual state and the theoretical equilibrium state 

 (see section 3-B-c of this Chapter). 



We shall therefore first in this section treat the system as quasi-stationary 

 and without accelerations. 



Non-linear effects (including effects of coupling with the astronomical tide) 

 will be left out of consideration here, but for the bottom stress, which may or 

 may not be linearized. 



The dynamical equations then become : 



9h'^-fUy + p-W,, = p-ira^-hp-^^, (15) 



gh ^ +fU, + p-Wty = p-Way - hp-^ ^, (16) 



where the astronomical forces and the astronomical effects have now been left 

 out. 



The equation of continuity is now : 



(^) Atmospheric pressure effect 



In the linearized problem the effects of atmospheric pressure and of wind- 

 stress may be treated independently. Therefore we leave Ta out for the moment. 



