The Three-dimensional Temperature Distribution and its Variation in Time 101 



process affects not only the vertical distribution of velocity within the current, but 

 also plays a considerable role for the distribution of the properties of the water mass. 

 The importance of such a mixing process, due to turbulent flow in a water mass, was 

 realized much earlier in oceanography than in meteorology. Gehrke (1909, 1912) 

 was the first to show that the mixing of the water masses in an ocean current must 

 give rise to a vertical transfer of heat. He found that this vertical heat transfer is pro- 

 portional to the product of the specific heat and the vertical temperature gradient, so 

 that it corresponds to the ordinary equation for the molecular thermal conductivity, 

 but with a coefficient which is dependent on the intensity of mixing and is consider- 

 ably larger than the coefficient for molecular thermal conductivity. Gehrke termed 

 this a "coefficient of turbulent mixing"; it has the dimensions [cm^ sec-^]. Following 

 Gehrke, Jacobsen (1913, 1915, 1918), in particular, has dealt in detail with the 

 "apparent" thermal conductivity and with the "apparent" diffusion which are con- 

 nected with turbulent processes. He pointed out that for all the processes initiated 

 by the mixing of the properties of the water (temperature, salinity and the content 

 in sea-water of other dissolved and suspended materials and of organisms) the tur- 

 bulent mixing coefficient should be the same and should be dependent only on the 

 intensity of the turbulence in the current. Through the turbulence also the flow mo- 

 mentum (impulse of the current) is affected by the "mixing" process, i.e. a vertical 

 equalization that manifests itself in the turbulent (apparent) viscosity. Already 

 Jacobsen has put forward the view that in the transfer of the small quanta of water 

 from layer to layer within the turbulent flow produces an immediate and complete 

 equalization of the momentum; however, complete equalization of the properties of 

 the water does not necessarily follow. This would imply that the "intensity of mixing" 

 of the momentum (turbulent viscosity coeflricient) must always be larger than that of, 

 for example, the temperature or the salinity (apparent thermal conductivity coefficient, 

 apparent diffusion coefficient). These views of Jacobsen appear to be confirmed by the 

 quantitative determination of these coefficients. 



Following these investigations which gave a deep insight into the nature and 

 efficiency of turbulent ffow, Schmidt (1917, 1917^, 1925) and Taylor (1915, 1918, 

 1922), at about the same time, carried out extensive work on turbulent flow and on the 

 phenomena connected with it, which has had a wide utility for the explanation of 

 several oceanographic phenomena. These started from the basic approach that due to 

 the random movement of individual small quanta of water in a turbulent flow there 

 is not only an equalization of the momentum in the direction of the largest velocity 

 gradient, but that every property can be transferred to an adjacent mass in the direc- 

 tion of its largest gradient. The simplest derivation of the most important and funda- 

 mental equation for the interchange of properties within a turbulent flow has been 

 given by Schmidt. Consider a horizontal unit area (1 cm^) in such a horizontal flow, 

 whereby the vertical direction z is counted positive upwards and negative downwards 

 of it (the zero point (z = 0) lies in the surface itself). Due to the turbulence of the 

 flow there will pass through this unit area a mass of water m^ upwards and a mass 

 ma downwards. Since, however, there is on the average a displacement of the water 

 only in a horizontal direction it follows that over a long period of time Hmy, = lima. 

 Every small quantum of water will, however, carry its properties with it during its 

 turbulent displacement. If one of these properties is designated by s (for instance the 



