Occasionally, formula (1) is represented as follows: 



„ doi Idt d^\dx dS „ , _ 



where the first term is the stability, determined by the temperature gradient and adiabatic temper- 

 ature change, and the second is the stability determined by the salinity gradient. 



UTERATURE: 60, 62, 77, 155. 



Section 28. Frictional Mixing 



A thin stream of fuchsin introduced into a slowly moving liquid flux in a glass tube, forms a 

 smooth straight thread. When the speed of this flux is increased the thread breaks. The broken 

 thread travels a certain distance, after which the liquids mix and become uniformly colored. The 

 first type of movement is called stratified or laminar, and the second, eddy or turbulent. Reynold's 

 theoretical considerations and experiments have shown that laminar movement is evidently possible 

 in nature only with the very slow movement of water in ground capillaries. In all other cases it is 

 a matter of turbulent movement, characterized by the following features: 



1. The speed at each point of the current fluctuates around its mean values with regard to 

 magnitude and direction. 



2. The speed of the current very close to the boundaries differs little from the overall speed 

 of the current. 



3. The motion depends only slightly on the viscosity of the liquid. 



The nature of turbulent motion has not been sufficiently explained, even for uniform liquids, 

 but its results are easily detectable from direct observations. Actually, only vertical and horizon- 

 tal velocity gradients can explain the presence, e.g. , in river currents, of the multitude of sus- 

 pended earthen particles with specific weights of 2. to 2. 8; these particles grow in size with an 

 increase of the velocity gradients. This fact is supported by the almost complete homothermy of 

 large, deep rivers and narrow straits with high current velocities, in spite of the diversity in their 

 heating and cooling conditions. 



Factors always exist in the ocean which cause velocity gradients, i.e. , agitation, currents 

 and tidal phenomena for the most part. 



With regular swells or agitation, the orbits of the particles become approximately circular, 

 and the velocity gradients are very small. But with wind agitation, particularly whitecaps, the 

 velocity gradients may attain very high magnitudes and thus cause mixing. 



The wind or wave mixing plays a role only in the surface layers of the ocean; it extends to the 

 bottom only in shallows and assumes particular importance off-shore, where the velocity gradients 

 increase. 



The ocean currents, on the other hand, usually cause high velocity gradients only in their 

 boundary surfaces, particularly at the bottom and off-shore. 



The tidal phenomena, i.e. , periodic vertical and horizontal oscillations of water masses, are 

 most important for turbulent mixing in the ocean. The velocities of tidal currents are, as a rule, 

 greater than those of steady or temporary ocean currents. Also, tidal phenomena extend throughout 

 the entire depth of the ocean, while ocean currents are usually confined to the surface layers and in 



67 



