For a velocity range of 4 to 16 meters per second (8 to 32 knots) at an 

 elevation of 10 meters, C is in the neighborhood of 1 to 2 X 10"^. 

 Higher values may be more generally applicable at higher windspeeds. 

 Wilson (1960), Roll (1965), and Wu C1969) give tabulations of Cjq for 

 airflow above water as determined by many experiments. 



Density stratification in the atmosphere, due either to cooling or 

 heating from below, will inhibit or encourage the f ormation of turbulence 

 and lead to changes in the turbulence term, (u'w'), in equation (4) 

 and consequently, to the form of K^ (z) . The resulting wind profile_ 

 will differ from equation (9). The changes are discussed in most text- 

 books on atmospheric turbulence (e.g., see Lumley and Panofsky, 1964 

 (ch. 3), or Kraus , 1972 (ch. 5)). They are not discussed here because 

 stratification in the airflow of a wind tunnel is difficult to estab- 

 lish or maintain. 



The boundary layer in which equations (4) to (9) are approximately 

 valid is defined as the layer in which the surface stress is much larger 

 than the pressure gradient or Coriolis acceleration terms in the equations 

 of motion. Kraus (1972, pp. 135-136) presented order of magnitude cal- 

 culations to show that in midlatitudes, the boundary layer thickness in 

 the atmosphere is unlikely to exceed 100 meters. Equation (9) is valid 

 only in the lower part of the boundary layer, perhaps to an elevation of 

 20 meters. Kraus concluded that the constant stress layer in the sea, 

 in which equation (9) could be valid, does not exceed a depth of 1 meter. 



3. Microscale Processes Involved in the Transfer of Momentum Between Air 

 and Water . 



Fundamentally, the friction between air and water should be considered 

 a downward diffusion of momentum from air to water. The diffusion process 

 in the atmosphere was discussed previously; consideration is now given to 

 the processes by which momentum is carried across the air-water interface. 



The momentum of the wind is developed in response to atmospheric pres- 

 sure gradients in a layer several kilometers in thickness. Removal of 

 momentum from the air is concentrated at the surface and in the lowest 

 10 to 20 meters of the atmosphere where the boundary layer equations are 

 valid for atmospheric flow. Thios , in general, the windspeed increases 

 with height. The horizontal momentum lost from the lowest layers is 

 replaced by turbulent diffusion from the free air, giving rise to the 

 logarithmic velocity profile for nonstratified flow. This momentum is 

 passed on to the solid earth or the sea through a combination of viscous 

 shears and pressure forces. 



Stewart (1961) first suggested that the essential difficulty in explain- 

 ing the variability in wind stress-windspeed relations was the neglect of 

 the effect of wave generation and decay as a means of transferring mechan- 

 ical energy and momentum from air to water. Hints that the stress mechan- 

 ism over water might be different from that over a land surface because of 



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