822 BOWDEN [sect. 6 



velocity in the tidal current. The shear also produces a gradient in the con- 

 centration S. Let the current be in the OX direction, u and S be the velocity 

 and concentration respectively at any depth, u and S their mean values from 

 surface to bottom and let u' = u — u, S' =S — S. Then u'S' represents a transport 

 of pollutant across a vertical plane perpendicular to OX due to the shear 

 effect. It may be shown that u'S' is always directed away from the centre of 

 the patch, so that it is equivalent to a longitudinal diffusion term. There is, 

 therefore, a contribution to the effective Kx from the shear effect, which 

 depends on the vertical eddy diffusivity Kz as well as on the vertical gradient 

 of velocity. The shear effect, which is probably of wide application in problems 

 of horizontal mixing in estuaries and coastal waters, is analogous to the effect 

 described by Taylor (1954) in treating the dispersion in turbulent flow through 

 a pipe and by Elder (1959) for the case of flow in an open channel. 



References 



Batchelor, G. K. and A. A. Townsend, 1956. Turbulent diffusion. Surveys in Mechanics. 



Cambridge Univ. Press, 352-399. 

 Bowden, K. F. and L. A. Fairbairn, 1952. Further observations of the turbulent fluctua- 

 tions in a tidal current. Phil. Trans. Boy. Soc. London, A244, 335-356. 

 Bowden, K. F. and L. A. Fairbairn, 1952a. A determination of the frictional forces in a 



tidal current. Proc. Roy. Soc. London, A214, 371-392. 

 Bowden, K. F. and L. A. Fairbairn, 1956. Measurements of turbulent fluctuations and 



Reynolds stresses in a tidal current. Proc. Roy. Soc. Loudon, A237, 422-438. 

 Bowden, K. F., L. A. Fairbairn and P. Hughes, 1959. The distribution of shearing stresses 



in a tidal current. Geophys. J., 2, 288-305. 

 Bowden, K. F. and J. Proudman, 1949. Observations on the turbulent fluctuations of a 



tidal current. Proc. Roy. Soc. London, A199, 311-327. 

 Bowles, P., R. H. Burns, F. Hudswell and R. T. P. Whipple, 1958. Sea disposal of low 



activity effluent. Proc. 2nd. Intern. Conf. Peaceful Uses of Atomic Energy, U.N., New 



York, is, 376. 

 Chamey, J. G., 1955. The Gulf Stream as an inertial boundary layer. Proc. Nat. Acad. 



Sci., 41, 731-740. 

 Charnock, H., 1959. Tidal friction from currents near the sea bed. Geophys. J., 2, 215-221. 

 Deacon, E. L., 1955. The turbulent transfer of momentum in the lowest layers of the 



atmosphere. C.S.I. R.O., Div. Met. Phys. Tech. Pap. No. 4. 

 Deacon, E. L., 1959. The problem of atmospheric diffusion. Intern. J. Air Pollution, 2, 



92-108. 

 Defant, A., 1954. Turbulenz und Vermischung im Meer. Deiit. Hydrog. Z., 7, 2-14. 

 Dietrich, G., 1950. Die anomale Jahresschwankung des Warmeinhalts im Englischen Kanal, 



ihre Ursachen und Auswirkungen. Deut. Hydrog. Z., 3, 184—201. 

 Dietrich, G., 1954. Einfluss der Gezeitenstromturbulenz auf die hydrographische Schicht- 



ung der Nordsee. Arch. Met. Geophys. Bioklirn., AT, 391-405. 

 Dietrich, G., 1957. Allgemeine Meereskunde. Gebriider Borntraeger, Berlin. 

 Doodson, A. T., 1940. A current meter for measuring turbulence. Hydrog. Rev., 17, 79-100. 

 Eckart, C., 1948. An analysis of the stirring and mixing processes in incompressible fluids. 



J. Mar. Res., 7, 265-275. 

 Eckart, C., 1955. Statistical hydrodynamics. J. Mar. Res., 14, 295-301. 

 Ekman, V. W., 1953. Studies on ocean currents. Results of a cruise on board the "Armauer 



Hansen" in 1930 under the leadership of Bjom Helland-Hansen. Geophys. Publ., 



19, (1), Pts. I andll. 



