810 BOWDEN [sect. 6 



concentration of a property produced in this way give rise to diffusion or 

 "mixing" along the gradient directions. These two processes interact to produce 

 the diffusion effects which are observed. 



Particular problems involving vertical or horizontal turbulence relate either 

 to the dynamical effects, which have usually been treated in terms of eddy 

 viscosity, or to the diffusion effects. In each case there are two possible methods 

 of treatment : 



(1) The turbulent fluctuations and the corresponding turbulent transports 

 may be considered directly ; 



(2) Distribution of mean properties of the water, e.g. velocity or salinity, 

 may be interpreted in terms of turbulence parameters, usually eddy coefficients 

 of viscosity or diffusion. 



These alternative approaches are considered in the following paragraphs. 



3. Turbulent Fluctuations and Turbulent Transports 



This section deals with investigations which are based on the direct measure- 

 ment of the turbulent fluctuations of velocity and, in some cases, also of 

 temperature. Oscillations of an apparently periodic character, such as those 

 associated with surface waves or tides, are excluded and the fluctuations under 

 consideration are understood to be those of a more irregular character. The 

 distinction, however, is not always clearly defined. Let x be the displacement 

 of a particle from a fixed point and u — dxjdt be its velocity. Then Eckart (1955) 

 distinguished between a "random oscillation", in which x^ remains finite as t 

 increases indefinitely, and a "random drift", in which x^ increases indefinitely 

 with time, although u'^ remains finite. The difference between the two oases 

 can be recognized in the form of the velocity spectrum as the frequency ap- 

 proaches zero. A general type of wave motion, as discussed in Chapter 15, 

 Section 3, corresponds to a random oscillation. Turbulent motion, on the other 

 hand, would appear to correspond to a random drift and it may be that this is 

 a valid criterion for distinguishing turbulence from wave motion. 



A record of fluctuations over a given length of time may always be represented 

 as a spectrum, in which a certain proportion of the total energy is associated 

 with each of a continuous series of frequency intervals. If a given narrow band 

 of frequencies contains an appreciable proportion of the energy, one may 

 speak, rather loosely, of fluctuations of this frequency as "occurring" in the 

 spectrum of turbulence. 



Measurements of velocity at a fixed point in the sea show the occurrence of 

 fiuctuations of a very wide range of periods, from the order of 0.01 sec, as 

 recorded by Patterson (1957) to a number of hours or even days, as reported 

 by Ekman (1953) or Swallow and Hamon (1960). It seems probable, therefore, 

 that the periods of fiuctuations found in a particular experiment will be limited 

 at the lower end only by the response-time of the instruments and at the upper 

 end only by the duration of the record. It may happen, however, that all the 



