350 Tides and Tidal Currents in the Proximity of Land 



In order to study the internal structure of a tidal current in relatively 

 shallow water, where frictional effects, originating at the sea bed and com- 

 municated through the water by internal stresses, will occur, measurements 

 were made of all factors in tidal currents a few miles from the coast (off Red 

 Wharf Bay, Anglesey). The results shall be briefly outlined as follows: Ex- 

 pressing the amplitude of the frictional force at the bottom in the form 

 F = kgU 2 , where U is the amplitude of the mean current from surface to 

 bottom, and q is the density of the water (see XI. 22), the results give the 

 coefficient k an average value of 1-8 x 10~ 3 , which agrees with the value 

 given on p. 346. The internal frictional stress in the water was found to 

 increase approximately linearly with depth from the surface to the bottom, 

 and the corresponding values of the mean eddy viscosity covered a wide 

 range of values (from 130 to 500 cm 2 sec -1 ). Previous estimates of the eddy 

 viscosity in tidal currents give a similar range. 



4. The Tidal Phenomena in Narrow Embayments 



The tides of coastal embayments derive their energy from the ocean tides 

 and are considered to be part of co-oscillating systems in which the period 

 is determined by the tide in the outer sea, while the detailed character of 

 the motion depends on the size and form of the enclosed water-masses. In 

 these small embayments the influence of the earth rotation is insignificant, 

 while the influence of friction cannot be neglected. Redfield (1950) has 

 recently given a method to analyse the tidal phenomena in these small em- 

 bayments. This method starts from the theory of free waves, which are 

 subjected to damping as they advance towards a coast on which they are 

 reflected, which theory was developed by Fjeldstad (1929; see also Sverdrup 

 et ah, 1946). The actual tide in the narrow embayment may be considered to 

 be due to two progressive waves of the same period travelling in opposite direc- 

 tions. The tide is treated a single cos-wave. One of these is the primary wave 

 originating in the open sea; the other is the reflected wave originating at the 

 closed end of the embayments, which can be considered as a barrier. At the 

 barrier the two waves are equal in elevation and are in phase. In a uniform 

 channel the elevation of the primary wave is given by 



r\ x = Acos(at~ , nx)e~ tix , 

 that of the reflected wave by 



rj 2 = A cos (at + xx) e 1 ** , 



(XI. 25) 



A is the amplitude of the waves at the barrier, a the change of the phase per 

 unit of time and t will be measured from the time of high water (H.W.) at 

 the barrier, when / = 0. k is the change in phase per unit of distance and x 

 is the distance measured from the barrier, where x = 0, /n is the damping 

 coefficient. 



The elevation of the water r\ at any time and place along the channel is 



