] 08 The Three-dimensional Temperature Distribution and its Variation in Time 



spreading of the Mediterranean water into the North Atlantic found a horizontal 

 exchange coefficient of 5-5 x 10^ cm^/sec. 



There is no doubt that the exchange coefficients for lateral mixing A^ and Ay are 

 about a million times larger than that for vertical mixing. The lateral mixing has thus, 

 despite the low values of the horizontal gradients for the different properties of sea- 

 water, at least the same importance as the vertical exchange. It can, however, be stressed 

 that the nature and inner mechanism of these two exchange processes are different; 

 the vertical mixing is small-scale, the lateral operates over a large space. It may be 

 expected that they are related to different ranges in the total turbulence spectrum 

 (see Chap. XIII, 3). 



The third special case is for mixing operating in all directions but without any dis- 

 placement of water in a particular direction ; it shows therefore the effect of mixing 

 alone unaffected by advection. In the two-dimensional case (.v- and r-directions) the 

 solution takes the form (Sverdrup, 1940) 



s = Sq + m 



cosh [a{h — z)] 

 cosh [ah] 



sin 27-v, 



whereby 



4/2 



For z = 0, that is at the surface of the sea, the distribution of a property s is 

 s = Sq -{- m sm {ttI21)x. 



Selecting, for example, h = 4 km, Sq = 0, m = 5 and AJA^ = 6 x 10^, then 

 a = 0-384 and Fig. 49 gives the distribution of s in an ocean of a horizontal extent 



Fig. 49. Distribution of a property "5" in the total ocean due to mixing alone (according 



to Sverdrup). 



2/ = 20,000 km. In this case it would reach from pole to pole. The abscissa in Fig. 

 49 is therefore divided into meridional degrees from 90° N. to 90° S. For a per- 

 sistent maximum accumulation of the property s at the surface of the sea in equa- 

 torial regions, the effect of mixing alone would in the stationary state force a distribu- 

 tion of j: in ocean space shown by curves of equal s in this representation. For a per- 

 sistent temperature difference at the sea surface along a meridian, essentially the same 

 as that produced by the combined effect of the solar and back-radiation, the effect of 

 a mixing process acting alone ovei the entire ocean would give a vertical temperature 

 distribution such as that shown by the isotherms in Fig. 49. The temperature decreases 



