SECT, 5] SURGES 635 



Subtracting (43) and (44) from (45) and (46) respectively and writing 



Ui = Uo + Uoi, 

 we obtain : 



^(Uoi, V^oi) = -^^ (47) 



VUoi = -~ (48) 



The boundary conditions for ^oi, Uoi are similar to those for ^o, Uo and for 



For finding Uoi one eliminates ^oi from (47) in the usual manner, by dividing 

 by h and taking the curl of both members of the resulting equation, thus 

 obtaining an equation for U which is analogous to (28) but for the absence of t 

 and the presence of dVoldt. 



Any boundary condition applying to ^oi is transformed into a condition for 

 Uoi by means of (47) ; the resulting condition is analogous to (32). 



If the sea has constant depth, it appears that the equation for Uoi derived 

 from (47) determines the field of curl Uoi, so that the problem reduces to the 

 well-known problem of finding a vector field Uoi if div Uoi and curl Uoi are 

 given, together with the boundary conditions. 



Further approximations can be obtained by formally replacing in the above 

 equations ^o, Uo, ^i, Ui by ^i, Ui, ^2, U2, respectively; and so on. 



As has been said before, the solution thus approximated is a solution on 

 which any free oscillation may be superposed if this should be required by 

 special initial conditions. 



A qualitative feature accompanying many wind surges in bays and partly 

 enclosed seas, such as the one shown in Fig. 9, is the phenomenon of the round- 

 going maximum. If the wind blows from the side of the main opening of the sea, 

 the water flowing inward from the opening during the rising stage of the surge 

 will experience a Coriolis force which causes an extra piling up on one side of 

 the area (the west side in Fig. 9). During the falling stage of the surge, water 

 flows back toward the opening, giving by the Coriolis force an extra piling up 

 on the other side. Thus it has often been found in such cases that the local time- 

 maximum of surge height travels counterclockwise along the surrounding 

 coasts. For the North Sea, for example, this phenomenon has been described 

 by R. H. Corkan (1950), J. and M. Darbyshire (1958) and G. Tomczak (1958) 

 and it has been confirmed by the experience of sea-level-height forecasting 

 services. In charts with iso-lines of disturbance height, it appears as a backing 

 of the iso-lines in the course of time (see Fig. 7). 



Locally, the wind effect may, in those areas where the equilibrium effect ^0 

 can be used as a first approximation, be written as the sum of ^o(0 ^^^ ^ 



