JSKCT. 5J TIDES 781 



The tides of tlie K2-constituent of an ocean which is bounded by parallels of 

 longitude separated by a distance of 60° and by the parallels of latitude 62.2°N 

 and S were evaluated by Rossiter (1958) using the difference method (Fig. 13). 

 In principle, when using this method, it is possible to take into consideration 

 the exact form of the coasts and depth distribution. 



Poincare (1910) developed an elegant mathematical theory of the tides 

 Avhich is principally applicable to the oceans ; practical applications of this 

 theory are not kno^n. 



6, Numerical Methods for Ascertaining the Tides and Tidal Currents. 

 Boundary- Value Problems 



Until recently the classical theory could not be applied to the true oceans. 

 Now, however, considerable scientific and practical interest exists in ascertain- 

 ing the tides of the sea quantitatively. This is especially true for the tides of 

 the open oceans, but nevertheless knowledge of the tides in marginal and 

 adjacent seas and estuaries plays a great part in the work of coastal engineers. 

 Therefore, it is to be understood that experiments have been undertaken to 

 solve these problems without using the methods of the classical theory. As 

 already mentioned, Defant was one of the first to renounce mathematically 

 exact solutions of the hydrodynamical equations and content himself with 

 numerical approximations. Defant's idea of replacing the differential equations 

 by difference equations is, therefore, particularly efficacious, because this 

 principle can be applied to the more general and complicated conditions found 

 on the Earth's surface. 



The special method of Defant is characterized in the one- and two-dimensional 

 cases by the elimination of the time f with the help of a time factor e"'"'. 

 Starting A\ith the linearized hydrodynamical equations, there result in the case 

 of a one-dimensional channel two equations from (6), the equation of motion 

 and the equation of continuity, 



d 



{-ia + r)u + g—{^-^) = 



■ (8) 



-i(jBs^+ ^{Qu) = 0. 



B is the width and Q is the cross-sectional area, both functions of x and |. 



In a two-dimensional case there are three equations, two equations of 

 motion and the continuity equation as written down in equations (6). In these 

 systems the velocity components may be eliminated, and the result is one 

 equation for f in each case 



d 



ial — ia + r)B^ + g t- 

 ox 



dx 



= (9) 



