Tides and Tidal Currents in the Proximity of Land 349 



friction corresponds also roughly to the phase of the current, but here the 

 variations are larger; the average is 9-3 x 10~ 3 , corresponding to a value 

 b = 1. A strict correlation apparently exists between the difference between 

 the phase of the current and the phase of the friction, and the values of k; 

 the latter increases with the former values. Grace uses a similar method to 

 determine the friction in the shallow Gulf of Suez. He finds k = 3-6 x 10 -3 or 

 b =011; this latter value is smaller than would be expected for a mean depth 

 of 44 m. On the other hand, the frictional influences prove to be very great, 

 so that they cannot originate from the ordinary bottom friction alone; it is 

 probable that they are increased by the existence of numerous cliffs and banks. 



All investigations show that Taylor's assumptions of the friction are capable 

 of giving its most essential effects on the tides, but as long as the friction- 

 produced changes in the tidal current are not more exactly considered, only 

 a rough approximation can be obtained. 



Investigations of this kind have been made in more recent times by Bow- 

 den (1947), Bowden and Proudman (1949) and Bowden and Fairbairn 

 (1952 a, b). Records of fluctuations in the speed of the tidal current (in the Mersey 

 estuary) near the bottom were obtained and compared with other records taken 

 with the current meter suspended freely at various depths. The fluctuations 

 covered a wide range of periods but could be separated into two main types : 

 "short period", having periods of the order of a few seconds, and "long period", 

 with periods from 30 sec to several minutes. The short-period fluctuations 

 correspond approximately in period to the waves, and their amplitudes are 

 of the same order of magnitude as the calculated wave-particle velocities. 

 From an exact analysis of the fluctuations it is concluded that the fluctuations 

 observed near the bottom are evidence of the turbulence associated with bot- 

 tom friction. It is believed to be the first time that the presence of turbulent 

 velocity fluctuations of this time-scale in the sea has been established ex- 

 perimentally. The long-period fluctuations show amplitudes, which increase 

 with the basic current and with depth and sometimes attain 04 of the basic 

 current; their features are consistent with their being turbulent in origin also, 

 although turbulence of the time-scale involved in this case would probably 

 be mainly horizontal. 



Later the component of turbulent velocity in the direction of the basic 

 current and across has been studied by means of several current meters placed 

 in the direction of the mean flow and across. The periods of the turbulent 

 fluctuations recorded varied from a few seconds up to several minutes, and 

 it appears that, as in other types of turbulence, a continuous spectrum of 

 fluctuations is present. It was found that the integral scale of the turbulence 

 in the direction of flow is of the order of 7 m, compared with 14 m, the mean 

 depth of water, whereas scales in the vertical and lateral directions are of 

 the same order of magnitude and of the order of one-third of the scale in 

 the direction of the mean flow. 



