TM No. 377 



A B 



Z*Q J* 





Terms A and B represent the transfer of mean flow kinetic energy derived 

 from the stress on the upper and lower boundaries. Term C is the rate of 

 transformation of kinetic energy of turbulent motions into or out of the mean 

 flow energy. 



The physical interpretation of equation (V-35) is illustrated by figure V-39. 

 The first two terms represent the transfer of mean flow energy at the mean free 

 surface 2 = ^ = and at Z = Z]_. Term A would normally vanish for Z± values 

 below the wave motion regime, since the u' and w J values diminish rapidly with 

 depth. If Z]_ = -D (i.e., at the bottom), the interaction of the mean flow with 

 the bottom roughness elements could provide a disturbance of the flow, but w* in 

 term B would essentially vanish. By evaluating the mean motion and the Reynolds 

 stresses at the levels Z = and Z = Z]_, one can determine the net flux of mean 

 energy through these boundaries. 



Equation (V-35) is derived directly from the Navier-Stokes equations for 

 turbulent flow (see appendix A). Other terms, which are brought about by the 

 viscous effects, can be neglected. In the absence of mean motion and, similarly, 

 in the absence of a mean shear, no energy can be transferred from the boundaries. 



It can therefore be argued that in a motionless volume of water subject to 

 a surface wind stress, the surface, being a fluid, must in time respond to this 

 stress, giving rise to some sort of a mean flow. This vertical distribution of 

 the stress and mean flow are the determining factors controlling the amount of 

 turbulent energy transformed into (or out of) the mean flow. Thus, the increase 

 of mean flow energy supplied by terms A and B in equation (V-35) will, in time, 

 force an increase in the shear S^/6?; in term C. This term may then increase 

 in magnitude until it approximately balances the influx terms A and B. The 

 result is a steady state condition, where incoming mean energy at the boundaries 

 is converted to eddy or wave energy. 



The magnitude and direction of the stress-induced mean motion is usually 

 smaller than the motions of tides or gross geostrophic flows. This explains 

 the sparsity of pure wind-induced current measurements. A system such as the 

 Gulf Stream may also gain mean kinetic energy and momentum from the contributions 

 of the air/sea boundary stress which has been integrated over large portions of 

 the ocean during long periods of prevailing winds through horizontal processes. 



137 



