346 Tides and Tidal Currents in the Proximity of Land 



tide in the main section will then seem to be the superposition of two ortho- 

 gonal standing waves. This simple case, which can also be computed, is 

 important in dealing with an actual sea (see p. 368). 



It is far better to assume that the friction is proportional to the square of 

 the average velocity of the tidal current (see vol. 1/2, p. 499). Taylor's as- 

 sumption for the frictional force has the form 



F = kQii\ (XI.22) 



if u is the mean velocity, g the density of the water and k a constant between 

 0002 and 0016, based on values observed in natural channels. If the bottom 

 configuration is irregular, this constant can have far higher values. The work 

 done by the frictional force is then 



In 

 xQifi = kgU 3 cos 3 — t . 



The mean value of cos 3 (2n/T)t for a full period is fjt, so that the amount 

 for the dissipation of the energy is 



in 



Taylor (1919) was the first to compute, using this relation, the loss of 

 energy of the tidal motion in the Irish Channel. According to observations, 

 the average U = 2\ knots = 114 cm /sec, and we obtain as the mean loss of 

 energy for this sea 1300 erg per cm 2 /sec. Taylor has also applied another 

 method to determine the loss of energy for the same sea. He computes the 

 quantity of energy which this section of the sea receives on one hand through 

 its southern entrance (Arklow-Bardsey Island) and, on the other hand, 

 through its northern entrance (Red Bay-Mull of Cantire). To this quantity 

 of energy E a has to be added to the quantity of energy E l which the tide 

 generating force transmits to the water-masses of the Irish Sea. The only loss 

 of energy R is caused by friction. As the tidal energy during a full period 

 neither increases nor decreases, R = E a J r E i . The numerical computation, 

 in the case of the Irish Sea, gives a loss of energy through friction of 

 1530 erg cm -2 sec -1 which agrees with the above-mentioned value as to the 

 order of magnitude. 



The principle of the conservation of energy teaches that, in every physical process, the trans- 

 formation of kinetic and potential energy of a system T and V always equals the work Q done by 

 the external force and to the loss of energy through friction E. If the first three quantities are known, 

 the fourth quantity can be computed. The kinetic and potential energy are given by the equations 



and 



V= hogrf, 



whereas Q = qhX{d^dt), when X represents the external force. The above-mentioned relation 



