Tides and Tidal Currents in the Proximity of Land 339 



It is obvious that the independent tides are small, except when the period 

 of the free oscillation comes close to the period of the forced oscillation and 

 resonance occurs. It is only in this case that this kind of tide becomes im- 

 portant in the more or less closed water masses of the adjacent seas. For 

 a basin which corresponds approximately to the dimensions of the North 

 Sea (/ = 800 km, h = 80 m, = 53° N. lat), we have 7} = 15-86 h, v = 1-29. 

 Consequently, the independent tide for M % will show two nodal lines: one 

 at the opening, the other one approximately 200 km distant from the inner 

 end. But the amplitude, at this end, will only reach about 2 cm. Things are 

 very different, when the condition of resonance is nearly fulfilled. If we select 

 the free oscillation period of the basin 7} = 18-9 h (for instance, like the 

 Red Sea with the Gulf of Suez and the gulf of Akaba), then for the semi- 

 diurnal tide v = 1-52, and with h = 450 m the amplitude at the closed end 

 will be 91 cm and there will be a nodal line of the standing wave in the centre 

 of the basin. 



For the co-oscillating tide the basic equations are the same as in (VI. 5 

 and 8), and the boundary conditions require that at the closed end (y = 0) 

 1=0, whereas at the opening (y = 1) we must always have r\ = Zcos(o7 + e), 

 i.e. the tide must always correspond with the tides of the open ocean. Then 

 the co-oscillating tide has the form 



. „ / smvny , . 



£ = Z — r cos(ot + e) , 



villi cosryr 



_ COS^TTV , , v 



v = Z ■ cos (at + e) . 



cosm 



(XI. 16) 



This part of the tide also has the character of a standing wave. There 

 will be resonance for the same values of v as in the case of the independent 

 tide. Figure 141, right, gives the distribution of the amplitude in a longitudinal 

 section of the basin for various values of v; here Z = 1. As the range of 

 the tide in front of the opening of the ocean basin can, in most cases, attain 

 very large values, it is apparent that the co-oscillating tide will be decisive 

 for the tides of the adjacent seas. 



The origin of the co-oscillating tide can be imagined to be the superposition 

 of an incoming tide wave and of the totally reflected wave at the closed end. 

 It is obvious that only the total reflection at the closed end produces a co- 

 oscillating tide in the form of a standing wave. 



(/S) Ocean basins with a complicated configuration. For ocean basins with 

 complicated orographical conditions the same methods can be used for de- 

 termining the independent and the co-oscillating tides as are used to determine 

 their free oscillation period (see Chapter VI/2, p. 154). The equations of motion 



22* 



