TM WOo 377 



motion in the X direction* Nov integrate (A~8ii-) and examine each term, for 

 its physical significance o 



If equation (A-S^) is integrated over a vertical strip in the S plane of 

 unit width (in the Y direction) and bounded at the sea bottom^ the result 

 gives the balance of kinetic energy of the mean flow across this section of 

 the current (see figure A-2)o The integration is carried out from the bottom 

 at g = -D to the surface g = 7 ( ytjir). The x coordinate of the strip is x^j 

 and the mean value of -w ^ over the averaging period T, is zero. If it is 

 assumed that the time-rate of change of mean kinetic energy is constant, then; 



>V B c X> 



Terms A and B represent contributions to the mean horizontal kinetic energy 

 due to horizontal flow caused by the fluid response to horizontal gradients 

 of hydrostatic and dynamic press-ore^ respectively^ Assuming hydrostatic 

 equilibrium of the mean pressure gradients^ teim A may be written: 





(A-86) 



The term *y^;C is the slope of the isobars and^ in general, may be associated 



with semi-diurnal tidal motions or ether types of motions having oscillatory ^ 



components whose periods are much larger than the period of averaging T« This , 



term could be evaluated from data obtained from appropriately spaced tide gaugeso j 



Evaluation of terai B in equation (A=85) requires measurements of the , 



variance of u(t) at two or more positions on the x axiSj^ and also as a fxinction i 



of depth,, From a practical point of view^ the term would be most difficult ! 



to determine experimentally-. In the region of a uniform wind field the 1 



horizontal gradient of the wind-driven perturbatip.Bs contributing to the ! 



variance 0^^^ would surely be small. 1 



Term C in (A-85) represents the contribution of pure fricticnal stresses j 

 to the mean kinetic energy^ The term must, of course ^ contribute negatively ; 

 to the mean kinetic energy^ since the viscous forces always act to impede 

 fluid flow; hence,, they tend to decrease kinetic energy- cf mean motiono The 

 frictional stresses occixr at the air-sea boundary and at the bottom. They 

 are brought about by viscous interaction of the wind with the waves and the 

 free surface^ and by water lute i-b,c: Lion with the bottom roughness elements » 



The integral C may be written as :• 



e 



A-IT 



