354 Tides and Tidal Currents in the Proximity of Land 



Redfield has tested this very practicable method of analysis on three 

 embayments: Long Island Sound, the Bay of Fundy and the system formed 

 by the Strait of Juan de Fuca and the Strait of Georgia. In all these cases 

 Redfield proves that the assumptions underlying the equations are valid. 

 He obtains a detailed description of these systems in terms of the distribution 

 of phase differences for the primary and reflected waves along the channel, 

 the velocity of their propagation and the coefficient of damping. An excellent 

 example of the application of this method is found in Redfield's analysis 

 of the Long Island Sound illustrated in Fig. 146 in which the data of mean 

 range of tides and time of H.W. are plotted on the co-ordinate system of 

 Fig. 144. The best fit of the data to the co-ordinate system is obtained by 

 assuming that the reflection occurs from stations 30 to 32 where the mean 

 tidal range is maximal at 7-2—7-4 ft. The observations made within Long 

 Island Sound proper, along the south side of Block Island Sound and in- 

 cluding Station 1 on the outer coast of Long Island fall closely along the 

 co-ordinate for a damping coefficient fi = 10. The phase difference of the 

 primary wave at each station relative to the point of reflection may be de- 

 termined from this diagram and the "co-phase" lines representing the advance 

 of the primary wave into Long Island Sound have been drawn in the upper 

 part of Fig. 146. The velocity of the primary wave is about 27 knots. In 

 Fig. 146 a number of stations appear where the range is greater than would 

 be expected if the value of fi is 1 0. These stations are all on the right-hand 

 side of the direction of propagation of primary waves and is an effect which 

 may be attributed to the rotation of the earth. The Bay of Fundy and the 

 system formed by the Strait of Juan de Fuca and the Strait of Georgia have 

 been analysed in a similar way. This simple method has proven its ad- 

 vantages (see also Redfield, 1953). 



5. Relations Between Tidal Current and Co-tidal and Co-range Lines 



The differential equations of motion give the most important relations 

 between the tides and tidal currents. From these relations we can deduct 

 the influence of islands and coastlines on the tides. Proudman (1914, p. 89; 

 1925, p. 243) has investigated these relations; however, he did not treat the 

 structure of the tidal current. 



The tide in a locality can be represented by 



r\ = Hcos((Jt—e) = ^ 1 cosct/ + ^sino-r 



in which ?; x and rj 2 are independent of time and high water occurs at the 



time t = e/a. 



Here 



?/i + >?2 = H 1 

 and 



- = tane. 



