TM NO. 377 



Term E iniplies '^ as a constant and could be evaluated with knowledge of the 

 surface and bottom values of the velocity gradient. [Hie value of-^^is, however, 

 probably not a constant | hence^ much difficulty arises in evaluating both E 

 and F, 



The integral D in (A=85)^ which has no dependence iipon emgpirical relations 

 as does C^ may be expressed asi 



® "^ H 



Teim G represents the flow of mean kinetic energy f rem the boundaries produced 

 by perturbations at the boundaries. At the sea sxirface the perturbations are 

 wind and the associated wind waves. At the bottom, disturbances can be pro- 

 duced by interaction of the mean motions with the gross bottom rotighness elements, 

 The sign and magnitude of G is dependent upon the direction and magnitudes of the 

 wind and the mean current Uo 



The integral H is the measTore off the rate of taransfer of mean kinetic energy 

 into (or out of) the kinetic energy of eddy motions « EvaLuafci^ of this term 

 requires knowledge of the variation of the Reynolds stress --^mV and the mean 

 flow u with depth. 



It should be noted that these equations were generalized in the sense that 

 no ass-uniptions were made of the causes of the stress terms (with the exception 

 of fluid viscosity). We only state that, if they exist, they contribute 

 to the momentum and kinetic energy of the mean flow in the manner shown. 



Going back to (A=85), assume that ^j;^Obut that the horizontal gradients 

 of the mean pressure and Eeynolds stresses are not zero. Taking the derivative 

 with respect to X of (A=85)2 



By again expanding and rearranging of terms: 



the kinetic energy being invariant in the X direction. Integrating (A'=89) gives: 



^ [_p"-f «r^ - ^^ f Jj - coa;$W)nT (a-90) 



A=l8 



