818 BOWDEN [sect. 6 



(1950) considered the energy acquired by the circulation from the wind to be 

 dissipated by lateral eddy viscosity in the western boundary currents. The 

 magnitude of the lateral shearing stresses required corresponded to a value of 

 Nh of the order of 5 x 10'^ cm^/sec. (The notation Nn and Kh will be used to 

 denote coefficients of horizontal eddy viscosity and diffusion when no distinc- 

 tion is made between the x and y directions.) Hidaka and other workers have 

 found that values of Nh from 10^ to 10^ cm^/sec are needed to account for the 

 observed features of the currents. An alternative explanation of a western 

 boundary current, such as the Gulf Stream, is to regard it as an inertial boundary 

 layer (Charney, 1955) in which the pressure gradients and Corolis forces are 

 balanced by field acceleration terms. Energy might then be dissipated in a 

 frictional boundary layer between the inertial flow and the coast. Alternatively, 

 energy might be abstracted from the main current by large eddies which 

 become detached from it and are themselves dissipated later. 



In view of the uncertainty about the significance of lateral shearing stresses, 

 methods of determining the Reynolds stress — puv directly are of special 

 interest. The analysis by Ichiye (1957) of GEK observations in the Kuroshio, 

 mentioned on page 813, gave values of —puv consistent with Ny of the order of 

 10^ to 10'^ cm^/sec. Stommel (1955) applied the same method to current measure- 

 ments in the Straits of Florida by Pillsbury in 1885 and found stresses corre- 

 sponding to Ny of the order of 10^ cm^/sec. 



A summary of data on horizontal eddy viscosity was given by Sverdrup 

 et al. (1942, p. 483) and methods of determining Nx or Ny from the observations 

 were given by Proudman (1953). The applicability of such methods to a 

 particular current system usually depends on the assumption that lateral 

 shearing stresses do, in fact, play a dominant part in its dynamics. 



Problems involving horizontal eddy diffusion are of two main types : 



(1) The maintenance of a steady distribution of a property, such as salinity, 

 in the presence of advection and a source or sink of that property. Periodically 

 varying distributions may also be included in this group. 



(2) The dispersion of a cluster of particles or the spreading of a patch of 

 pollutant, initially concentrated within a small volume. 



Problems of the first type arise in many oceanographic investigations and 

 are treated, almost invariably, in terms of effective eddy coefficients Kx or Ky, 

 which are, in general, functions of position and also of the scale of the process 

 under consideration. The methods of analysis involve special solutions of the 

 diffusion equation : 



dS 8S dS d /' ^ dS\ 8 /^^ dS\ 



Typical examples of such investigations have been given by Sverdrup et al. 

 (1942), Proudman (1953) and Dietrich (1957). 



The average rate of increase of the separation of pairs of particles, or marked 

 elements of fluid, is the problem treated directly in Richardson's "neighbour 



