WIND CURRENTS AND WIND WAVES 121 



obtain more measurements of wind profiles, because results in fluid 

 mechanics can be successfully applied in the study of such profiles. 



The theoretical equations for the relations between stress and wind 

 velocity are valid only if the stability of the air is nearly indifferent. 

 Under stable or unstable conditions the wind profile and the relation 

 between wind and stress will be altered. A study of wind profiles at 

 different stabilities of the air is therefore of great interest. 



Piling Up of Water Due to the Stress of the Wind 



At the sea surface the stress that the wind exerts on the water, Ta, 

 must balance the stress that the water exerts on the air. The latter has 

 the components iJLe,o(dvx/dz)o and iie,o{dvy/dz)o, where He now means the 

 eddy viscosity of the water. Therefore, 



r„ = -Me.o (J-)^ and r„, = -M..o (j"); (VII, 9) 



This relation is useful in a study of the effect of wind based on the equa- 

 tions of motion of the water. Including the terms that determine friction 

 due to vertical turbulence and assuming that acceleration can be neg- 

 lected, the equations of motion take the form 



'^l) f( (VII, 10) 



-\pv. + gpt,.y + ^ I^M. -^j = 0. 



Here the geometric slopes of the isobaric surfaces are introduced. Inte- 

 grating the equations between the surface and the bottom and considering 

 that the stress, r^, which the current exerts on the bottom has the 

 components 



rd,x = ^ie,d(dvx/dz) and Td,y = fieAdvy/dz), (VII, 11) 

 one obtains 



Ta.x + Td.x = —^ L P^ydz — L gpip.xdz, 



ff fi . (VII, 12) 



Ta,v + Td.y = ^ Jo P^xC?2; — Jq gpip,ydz. 



Consider next a channel which is so narrow that transverse motion 

 can be neglected, and place the x axis in the direction of the channel 

 (Vy = 0). Assume furthermore that the water is homogeneous, so that 

 the inclination of the isobaric surface is independent of depth. The first 

 of the above equations is then reduced to 



Ta,x + Td.x = —gpip.jd; (VII, 13) 



that is, the stresses acting in the direction of the channel at the upper and 



