Favre and Coantia 



d) Transfer of kinetic energy across the turbulent boundary layers 

 on both sides of the interface, of which the most obvious effect 

 is the generation of waves. 



Information on these nnechanisms can be gathered in many books, 

 ranging from meteorology (e.g. Brunt [ 1939] , Haltiner and Martin 

 [ 1967] , Roll [ 1965] ) to oceanography (e.g. Lacombe [ 1965] , 

 Phillips [ 1966] , Sverdrup [ 1957]), or devoted to atmospheric tur- 

 bulence (e.g. Lumley and Panofsky [ 1964] , Monin and Yaglom [ 1966] , 

 Priestley [ 1959]). One of the first steps of our program has been to 

 attempt to review the physical laws and equations governing the 

 ensemble of these phenomena (see Coantic [ 1968]). 



The main conclusion that can be reached is that, although the 

 above types of transfer have been analyzed and listed separately, 

 they are not independent, and the key of the problem lies in their 

 reciprocal interactions. For instance, processes a) and b) set In 

 action very large amounts of energy, whereas c) and chiefly d) are 

 responsible for much smaller exchanges. However, the kinetic 

 energy transfer, which enters as the smallest term in the energy 

 bcdance, strongly influences the turbulent evaporation and convection 

 processes. In fact, except for certain radiation effects, air-sea 

 interactions are essentially governed by turbulence. 



This is only one aspect of the aforementioned reciprocal Inter- 

 actions. Other ones will appear, for instance, when considering the 

 boundary conditions for the various variables at the Interface, or 

 when expressing the conservation of the different energy fluxes, as 

 schematized on the lower part of Fig. 1. Furthermore, two most 

 important peculiarities are displayed when comparing the present 

 case to the more classical problem of slmioltaneous heat, mass and 

 momentum exchange between a fluid flow and a more or less rough 

 surface. In the latter case, the turbulent convectlve processes, 

 if not completely understood, are sufficiently well known to allow a 

 good estimate of the various transfer rates. However, the methods 

 of computation therein developed are not applicable here for two 

 main reasons: 



- On one hand, because the boundary Is no longer static, and pos- 

 sesses "dynamic rugosities" capable of yielding and absorbing 

 momentum with large variations of the ratio of the tangential shear 

 stresses to the normal pressure forces. This fact will have conse- 

 quences difficult to ascertain, not only upon the dynamical exchange 

 mechanism but also upon the degree of "Reynolds analogy" be- 

 tween this process and those concerning exchange of sczilar vari- 

 ables. 



- On the other hand, because, due to the well known stratification 

 effects In the atmosphere, heat and humidity can no longer be con- 

 sidered as "passive scalar containments. " This means that the 

 turbulent structure of the boundary layer, and the transfer rates 

 themselves, are strongly modified by the direction and Intensity 

 of the vertical heat and humidity gradients. 



40 



