Long Waves in Canals and Standing Waves in Closed Basins 231 



Table 28. Surface disturbances at the east (x = 0) and west (x = a) ends 

 of the southern shore in a rectangular gulf oriented from North to South 



(£, the displacement of free surface from its undisturbed position ;v, the coefficient of eddy viscosity, T, 

 the wind stress; a positive T x will mean a westerly wind and a positive T y a wind from the south. 



According to Goldsbrough, 1954) 



I. Transverse wind. Values of $qv/T x 



In the north where the effects of south 

 Closed end (southern shore) boundary are evanescent 



II. Longitudinal wind. Values of £ovlT y 



In the north where the effects of southern 

 Closed end (southern shore) boundary are evanescent 



Theoretical investigations of this kind are, without any doubt, of great 

 importance as far as the understanding of the problem of storm surges is 

 concerned; however, one should be careful in applying the results obtained 

 to the actual process in nature because of the simplifications in the models. 



In studying the problems suggested by coastal flooding the effects of the 

 interaction between the tide and surge are important. The maxima of the 

 highest surges observed up to the present time have occurred nearer to the 

 time of tidal low water than to the time of tidal high water. Since the timing 

 of the meteorological conditions which generate the surge is independent 

 of the timing of the astronomical tide, it would appear that the characteristic 

 just noted must be of hydrodynamical origin. Proudman (1955a, b) and 

 Doodson (1956) have studied this problem very thoroughly. Proudman 

 has given a theoretical investigation of the distribution, along an estuary, 

 of a combination of tide and surge which have been generated in the open 

 sea. For a single progressive wave, the height of a surge whose maximum 

 occurs near to the time of tidal high water is less than that of a surge whose 

 maximum occurs near to the time tidal low water, and it decreases as the 

 range of tide increases. This is in agreement with the observations; besides, 

 the friction seems to be the cause of these differences. With a standing oscilla- 

 tion on the head of the estuary, when the primary surge rises to its maximum 

 more rapidly than it falls from it, and when this maximum occurs near to 

 the time of tidal high water, the effect of shallow water is to make the surge 



