SECT. 2] SMALL-SCALE INTERACTIONS 45 



To measure the rate of transfer of some property between sea and atmosphere 

 we are fortunately not under the necessity of making observations at the surface 

 of separation itself. Except when conditions are changing rather rapidly, the 

 rate of accumulation of the property in the lowest few metres of atmosphere is 

 negligible in comparison with the flux traversing the layer to affect the atmos- 

 phere above. The existence of this layer of very nearly constant flux makes it 

 possible to obtain the requisite transfer rates by suitable measurements at 

 convenient heights above the sea. 



A vertical turbulent flux of the entity *S^, whose measure per unit mass of air 

 is s, is accompanied by two manifestations : 



(^ ) Turbulent fluctuations of S from its mean value s at the level of measure- 

 ment, these fluctuations being correlated with the vertical component of eddy 

 motion. 



{ii ) A vertical gradient of s. 



These phenomena provide the two main ways in which knowledge of the 

 vertical fluxes may be derived, the flrst giving rise to the eddy- correlation 

 technique and the second to the "aerodynamic" or "profile" methods. ^ 



A. The Eddy -Correlation Technique 



Considering unit area in a horizontal plane, the eddy flux {Fs) of S is given 

 by the covariance of the fluctuations of s and of the product of vertical velocity 

 component, w, and density, p. The relation is 



Fs = ipwYs' ~ pw's', (1) 



where the bar denotes the average over a period of time at a fixed point and 

 primes denote instantaneous departures from w and s appropriate to the same 

 period of time. In the particular case of momentum transfer the above expres- 

 sion becomes the familiar Reynolds' formulation of the turbulent stress. 



Direct measurements of eddy flux can, therefore, be made using instruments 

 of sufficiently rapid response. Fortunately it is not necessary to take full 

 account of all the higher frequencies present in fluctuations of w and s. This is 

 a consequence of the smaller scales of eddy motion being generated by the 

 larger scales : in the progressive handing down of energy from large eddies to 

 smaller ones, the anisotropy of the large eddies, which enables them to effect 

 momentum or heat transfer, etc., is rather rapidly lost. This is well illustrated 

 by the spectral distribution curves given by Panofsky and Deland (1959) of 

 which Fig. 1 is an example. It is apparent that a nearly ten-fold greater 

 responsiveness is needed to take account of all the vertical eddy energy (full 

 line spectrum of Fig. 1) than is requisite for the flux measurement (broken 



1 There is, however, another method, outhned by Deacon (1959), which relates the 

 intensity of the higher frequencies in the turbulent fluctuations of velocity and tempera- 

 ture to the respective fluxes. This approach, which has given promising results in pre- 

 liminary work over land, may have considerable advantages for use at sea. 



