General Theory of Ocean Currents in a Homogeneous Sea 397 



completion. This theory leads to the same 4/3-power law for the turbulent exchange 

 coefficient which was previously derived from observations. With some modifications 

 this theory can be applied to large-scale processes occurring with oceanic currents, 

 and offers the possibility of obtaining a picture of the spectral distribution of energy 

 in oceanic turbulence. It is thus of a considerable interest for oceanography. 



The semi-permanent wind systems such as the trade winds, the prevaihng westerlies 

 of temperate latitudes, and furthermore, the aperiodic air currents of the extra 

 tropical pressure disturbances, give rise to large-scale movements in the surface layers 

 of the ocean due to the shearing stresses acting on the sea surface. Thereby, these 

 shearing stresses tend to increase the kinetic energy of the currents produced. However 

 the mean kinetic energy of the ocean currents remains largely constant (quasi- 

 stationary conditions) so that finally as much energy is dissipated in heat as is gained 

 by the work done by the shearing stress of the wind. Ocean currents which initially 

 show large-scale turbulence tend to break up into vortices which subsequently 

 degenerate into smaller and smallest vortices. This proceeds until finally the smallest 

 vortices are formed, which are so small that their energy is converted in irreversible 

 processes by molecular viscosity into heat energy. An exact dynamic explanation of the 

 reasons why the large ocean currents break up into turbulent currents, with more or 

 less large vortices of widely varying size, has not yet been given. However, the em- 

 pirical facts of their existence have been shown by synoptic surveys, for instance, in the 

 more recent Gulf Stream investigations. 



A complete spectrum of vortex sizes certainly exists. This spectrum is necessary for 

 the dispersion of the kinetic energy of the ocean currents continuously supplied by the 

 shearing forces of the wind. In practical oceanography it has long been recognized 

 that the concept of the mean velocity of the oceanic currents is rather dependent on 

 the length of the time interval over which its value was determined. The same applies 

 for space-means of the current intensity. This leads to the expectation that the mag- 

 nitude of the turbulent coefficients also depends fully on what kind of evaluation of the 

 mean has been used. The concept of a turbulence coefficient is absolutely meaningless 

 if the way in which the mean was found is not specified. This can be seen already from 

 the greater magnitude of the turbulence coefficients the greater the dimensions of the 

 movements under consideration; a fact which could not be explained in earher work. 



The Weiszacker-Heisenberg statistical theory provides information on the fre- 

 quency distribution of the energy in different size-intervals of turbulent vortices, on 

 the way in which the mean velocity depends on the type of mean taken, and lastly on 

 the dependence of the turbulence coefficients on the type of mean taken. 



If Ln is the side of a square over which the nih. mean is taken then according to 

 Weiszacker the spectral law is, for the turbulent velocity distribution : 



z7„ proportional to L)^^, 



for the turbulence coefficient: 



7j„ proportional to L,^^ 

 and for the turbulent energy distribution: 



En proportional to L^J^. 



