18 PHYSICAL PROPERTIES OF SEA WATER 



space of velocity, temperature, and salinity, it follows that the corre- 

 sponding gradients cannot be determined and that no basis exists for 

 application to the processes in the sea of the coefficients of viscosity, 

 thermal conductivity, and diffusion that have been determined in the 

 laboratory. Since only certain average gradients can be determined, the 

 problem of the effect of turbulence has to be approached in a manner 

 similar to that employed when dealing with the effect of atmospheric 

 turbulence. In order to illustrate this approach, let us first consider the 

 viscosity. 



In the case of laminar flow in the a:-direction only, the dynamic 

 viscosity, /x, is defined by the equation r = /x dv/dn, where r is the shearing 

 stress and dv/dn is the velocity gradient normal to the surface upon which 

 the stress is exerted. In the case of turbulent flow, a dynamic eddy 

 viscosity, fie, can be defined in a similar manner: r = jue dv/dn, where r now 

 is called the Reynolds stress and where dv/dn represents the gradient of 

 the observed velocities. The numerical value of the eddy viscosity 

 depends upon the size and intensity of the eddies — that is, on the magni- 

 tude of the exchange of masses between adjacent layers. The numerical 

 value of He also depends upon how the ''average" velocities have been 

 determined — that is, upon the distribution in space of the observations 

 and upon the length of the time intervals to which the averages refer. 



The definition of the eddy viscosity in the above manner appears 

 purely formalistic, but it is based on the concept that masses leaving one 

 layer carry with them the momentum corresponding to the average 

 velocity in that layer, and that by impact they attain the momentum 

 corresponding to the average velocity of their new surroundings before 

 again leaving them. Thus, fie is an expression for the transfer of momen- 

 tum of mean motion. This transfer is much increased by the turbulence, 

 as is evident from the fact that the eddy viscosity is many times greater 

 than the molecular viscosity. 



In both the atmosphere and the sea it has been found practicable to 

 distinguish between two types of turbulence — vertical and horizontal. 

 In the case of vertical turbulence the effective exchange of masses is related 

 to comparatively slight random motion in a vertical direction or, if the 

 term ''eddy motion" is used, to small eddies in a vertical plane. Actu- 

 ally, the eddies are oriented at random, but only their vertical components 

 produce any effect on the mean motion. The corresponding eddy viscos- 

 ity has been found to vary between 1 and 1000 c.g.s. units, thus being one 

 thousand to one million times greater than the molecular viscosity of 

 water. In the case of horizontal turbulence the effective exchange of 

 masses is due to the existence of large quasi-horizontal eddies. The 

 corresponding eddy viscosity depends upon the dimensions of the system 

 under consideration and has been found to vary between 10^ and 10^ c.g.s. 

 units. 



