338 



Tides and Tidal Currents in the Proximity of Land 



7) = 0. If we put: v = 7}: T„ = alien in which 7} == 2l/\/gh is the period 

 of the basin if it would be completely closed and T M = 2n\o the period of 

 the force, we obtain for this independent tide: 



1 = 



rj = 



2m 



a 2 cos vjt 

 mT^gh 



sm\vnys\\\vji{\ — I y) cos (ot + e) 



2ng cos vji 



smv7t(y— l)cos(o7 + e) 



(XI. 15) 



It has the character of a standing wave. If v becomes \, §, §-, etc., I and rj 

 become infinite. This means resonance, which, in the absence of friction, 

 means that the amplitude of the motion increases so rapidly that the solution 

 becomes unapplicable. If vn is very small, i.e. if the period of the generating 

 force is large compared with the period of the slowest free oscillation of the 

 basin, we obtain for tj in first approximation: 



m 



rj = —l(y— l)cos(o7 + £) . 



This is a simple oscillation with a nodal line at the opening, as if the water 

 were without inertia. 



Closed eno 



Opening 



#?•* °° Sed Cnd 

 03 



Fig. 141. Distribution of the amplitude in a longitudinal section of a rectangular basin 

 of uniform depth for the independent tide (left) and the co-oscillating tide (right). 



The left part of Fig. 141 gives the distribution of the amplitude in a basin, 

 for different values of v, assuming that the factor mT^c^ng = 1 cm. The 

 amplitudes of the independent tides increase, when the basin becomes deeper. 

 According to (VIII. 7) mjg = l-235xl0 -7 for the combined lunar and solar 

 tides at the equator, so that the factor becomes 0-0273]/ A in cm. In the 

 latitude we must multiply mjg by cos<p. 



