394 General Theory of Ocean Currents in a Homogeneous Sea 



on vortices of smaller dimensions that has to be regarded as the turbulence of the 

 current. The origin of the oceanic turbulence must thus be traced back to the con- 

 ditions of formation of the ocean current, and this can definitely be considered to have 

 been done, since the conditions which prevail initially during the formation of the 

 current are certainly scarcely of the type that could be described by simple functions 

 of the velocity distribution. On the contrary, everything indicates that during the forma- 

 tion of a current due to the complicated distribution of the shearing stresses of the 

 winds, the ocean current looks right from the beginning rather confused in vertical 

 and horizontal direction, so that a priori there is a very large probability that in the 

 future the resulting current will attain a form which will fall within the general concept 

 of turbulence. 



Turbulence is not a form of motion that can maintain itself indefinitely. The kinetic 

 energy of the current is continuously converted by the molecular viscosity into heat. 

 If the current is not continuously supplied with fresh energy, it must in time die away. 

 In the ocean, the currents are continually supplied with energy by the tangential 

 shearing forces of the winds so that here steady turbulent currents are possible. This is 

 of particular importance to the nature of ocean currents which are recognized as 

 essentially quasi-stationary phenomena by observations. 



Turbulence and mixing in vertical direction and also lateral turbulence of the ocean 

 currents were already discussed in § III dand e of Pt. I of this volume. Lateral mixing 

 is on a much larger scale than the vertical ; the turbulence elements are of considerably 

 larger dimension, so that the eddy viscosity and eddy diffusion coefficients are very 

 large. The ratio of vertical to lateral mixing coefficients is of the order of 10^ to 10'. 

 It can be shown both experimentally and by observation that there is a "continuous 

 spectrum" of mixing and turbulence coefficients extending from the molecular vis- 

 cosity coefficients to values for the eddy conductivity of 10^^ (one billion) or more 

 (Richardson, 1926). 



In a turbulent current where u is the velocity at a certain point and varies with time, 

 the basic velocity is defined as (time interval 7") : 



1 r 

 U=^\ u(t)dt 



and further the supplementary turbulent velocity as u' = u(t) — U, whereby 



1 r 



- u'(t) dt = 0, 



the intensity of the turbulence is given by 7 = 1/\/{(m')-} and its kinetic energy by 

 E = ip(M')^.* These quantities characterizing the turbulence of the flow depend of 

 course on the length of the time-interval T, and in fact a sufficiently large value for 

 T has to be selected or these quantities lose their meaning altogether. In laboratory 

 experiments in wind tunnels this requirement can always be closely approached, but 

 whether this is also the case for oceanic water masses is difficult to judge. If T is less 

 than a few hours then the »'(0-values will include terms for the small-scale turbulence 

 such as local mixing, while the basic velocity U will include the long-periodic variations 



The bar above a quantity indicates its mean value taken over the time-interval T. 



