TM No. 377 



wave generation indicate that a linear system is not very well suited to 

 describe the energetics of wind waves. 



Reynolds Stresses in Ocean Waves 



Certain quantitative features of the dynamic energy content of the surface 

 layer have been depicted through analysis of the wave meter observations. Space 

 variable and time variable distributions of turbulent kinetic energy and their 

 accompanying spectra have been portrayed and associated with wind wave conditions. 

 A more important and more difficult question remains to be considered. What 

 deductions can be made regarding momentum and kinetic energy transport through 

 and within the regime of the ocean surface wave motions? 



Consider first the application of Eulerian wave particle velocity measure- 

 ments in describing the momentum flux within the dynamic regime of wind wave 

 motions. A simple intuitive model can be used to consider the flow of momentum. 

 Assume a volume of ocean bounded at the surface by 2 = 07 (t) = and at the 

 bottom by Z = -D, and having a unit width in the Y direction. Assume also a 

 steady wind that generates wind waves in the positive X direction as shown in the 

 figure V-39* The wind blowing across the surface exerts a mean stress on the 

 water. Now a mean stress can occur only if there is a mean vertical shear of 

 horizontal velocity between the wind and the water surface. Likewise, the stress 

 exerted at the surface must couple with the subsurface water, giving rise to a 

 mean velocity gradient and an internal flow of horizontal momentum. 



What then are the dynamics of motion occurring at a point just below the 

 surface waves that are being subjected to the stress of the wind? Assume, at 

 this point, that a Reynolds stress does exist, given by: 



T=*f"2iV > (v-30) 



where p is the density of sea water, which is assumed constant. 



The Reynolds stress function may be interpreted in two ways: as the time 

 averaged horizontal shear stress or force existing across a unit horizontal 

 area, or as a downward flow of horizontal momentum through a horizontal unit 

 area per unit time. 



Thus, assuming the proper measurement of u* and w r at a given point, the 

 Reynolds stress delineates the shear stress, and hence the direction and magni- 

 tude of the flow of momentum imparted at the sea surface. 



To better visualize this, consider a thin horizontal slab, of thickness ©£ 

 and of unit width in the Y direction, situated within the water volume (see 

 figure V-39)« If - PU'ui is "the momentum flux per unit horizontal. area, then 



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