OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 93 



studied. In many oceanographic problems, however, knowledge of the 

 periodic current is not essential, but knowledge of the currents that 

 transport water over long distances is important. Currents related 

 to the distribution of density can be computed from the more easily 

 observed temperatures and salinities by following the procedure that will 

 be discussed in detail in the following pages, and wind currents can be 

 examined theoretically. Herein lie the value of the application of 

 hydrodynamics to oceanography and the necessity of familiarity with 

 this application if all possible conclusions are to be drawn from the 

 observed distributions. 



Equations of Motion Applied to the Ocean 



General Equations. When dealing with ocean currents the same 

 forces have to be considered as those which must be taken into account 

 when discussing the dynamics of the atmosphere, namely (1) gravita- 

 tional forces, (2) forces due to pressure gradients, (3) the deflecting force 

 of the earth's rotation, and (4) frictional forces. In a left-handed rec- 

 tangular coordinate system with the positive 2-axis directed downward 

 the equations of motion have the form 



dvx dVx . dVx . dVx , dVx ^_ . dp 



dVy dVy . dVy . BVy . SVy O r^ ' ^P I 73 /XTT l\ 



dvz ^v^ dVz , dv, . dVz „^ . , ^P i d 



dt dt dx dy dz dz 



The symbols used have the meaning: 



Vx, Vy, Vz, the velocity components along the coordinate axes 



Ve, the horizontal velocity toward the east 



12, angular velocity of rotation of the earth, 0.729 X 10~'* 



<p, geographic latitude 



a, specific volume of the water 



p, pressure 



Rx, Ry, Rz, components of the frictional force per unit volume 



g, acceleration of gravity. 



In the above form the equations are applicable to conditions in the 

 Northern Hemisphere. For the Southern Hemisphere the sign of the first 

 term on the right-hand side of the first two equations, the term represent- 

 ing the horizontal components of the deflecting force, must be reversed. 

 Motion in the Circle of Inertia. If the horizontal component 

 of the deflecting force of the earth's rotation is the only acting force, the 

 equations of horizontal motion have the form 



