816 BOWDEN [sect. 6 



Sverdrup et al., 1942, p. 480). From measurements at three levels, 21, 51 and 

 126 cm above the bottom, with velocities from 15 to 26 cm/sec, they deduced 

 that the logarithmic law was valid and that the bottom was rough, with a 

 roughness length 20 = 2 cm. Mosby (1947, 1949), using the cup-wheel current 

 meter described on page 811, recorded the current simultaneously at 12 

 levels, from 9 to 249 cm above the bottom in the Alvaerstrommen. From 30- 

 min averages, it appeared that the profile was approximately logarithmic, 

 although there were considerable variations from one period to another. 



Lesser (1951) made observations at four levels, 20, 40, 80 and 160 cm above 

 the bottom, using four Ekman current meters mounted on a tripod. The 

 measurements were made in homogeneous water, in depths of about 45 m, 

 on three types of bottom. Interpreting the data in terms of the logarithmic 

 law, Lesser deduced that, in two cases, with bottoms of gravel-sand and mud- 

 sand respectively, the flow was rough with 20 from 1.3 to 1.6 mm. In the third 

 case, with a mud bottom, the flow appeared to be smooth, but in this case the 

 velocities were very low, reaching 12.7 cm/sec at 160 cm. 



Observations were made in a tidal current off Anglesey by Charnock (1959), 

 using an instrument consisting of five cup-wheels at heights from 30 to 200 cm 

 above the bottom. Most of the velocity profiles recorded were approximately 

 logarithmic and corresponded to hydrodynamically rough flow with zq from 1 

 to 3 mm. The frictional stresses estimated in this way were in reasonably good 

 agreement with those determined by other methods in the same area (Bowden 

 and Fairbairn, 1952a and 1956). Bowles et al. (1958) have described observations 

 made with the same equipment at a f)osition in the English Channel, south of 

 Arish Mell Gap. The velocity profile was found to follow the logarithmic law, 

 with values of zq which were rather variable but averaged 2 mm. 



The apparatus designed by Charnock was also used by Bowden, Fairbairn 

 and Hughes (1959), in conjunction with a Doodson current meter for current 

 measurements at greater distances from the bottom, to determine the variation 

 of shearing stress with height. This investigation yielded estimates of Nz at 

 various depths which indicated that its value was somewhat greater near mid- 

 depth than nearer the surface or bottom, reaching the order of 300 cm^/sec 

 during the flood and 150 cm^/sec during the ebb. In the case of tidal currents in 

 homogeneous water it might be expected on dimensional grounds that the 

 maximum value of Nz would be proportional to Uh, where U is the amplitude 

 of the tidal current and h the depth of water. From the Anglesey data, the 

 average value of (NzUaxJUh is 2.5 x 10-3. 



C. Tidal Mixing in Coastal Waters 



It has been known for many years that in shallow areas with strong tidal 

 currents the water remains homogeneous throughout the year, whereas in 

 areas of similar depth with weaker tidal currents a thermocline develops in the 

 summer months. In such cases there are two sources of vertical turbulence : 

 that due to the wind being most intense near the surface and decreasing with 



