OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF AAASS 97 



fulfilled everywhere along the boundary surface, and defines therefore the 

 shape of that surface in the same manner that (VI, 6) defines the isobaric 

 surfaces. 



The dynamic energy equation is obtained by considering that the work 

 done by a force is equal to the product of the force and the distance 

 traveled in the direction of the force. Multiplying the equations of 

 horizontal motion by Vx and Vy, respectively, and adding, one obtains 



P 

 because 





and because the terms containing the deflecting force cancel. On the 

 left-hand side of the equation stands the increase of kinetic energy per 

 unit mass. On the right-hand side stands the sum of the work per unit 

 mass performed by the forces due to pressure distribution and friction. 



The equation is of small interest because it tells only that the increase 

 of kinetic energy per unit mass equals the work performed per unit mass 

 by the acting forces, but, combined with the thermodynamic energy equa- 

 tion, it becomes of importance. The complete derivation is given by 

 V. Bjerknes and collaborators; only the result for a system that is 

 enclosed by solid boundaries is stated here: 



^^ ^ (i^ -i- $ -}- ^) -f r r j {aRxV, + aRyVy)dx dy dz, (VI, 11) 



dt dt 



where W is the amount of heat added to the system, K is the total kinetic 

 energy of the system, $ is the potential, and E is the internal energy. If 

 the total energy of the system remains unaltered, the amount of heat 

 added in unit time must equal the work per unit time of the fractional 

 forces. If, on the other hand, no heat is added, the work of the frictional 

 forces must lead to a change of the total energy of the system. 



Practical Application of the Hydrodynamic Equation for the 

 Computation of Ocean Currents. In their above form the hydro- 

 dynamic equations are still too complicated to serve practical purposes, 

 and hence they must be further simplified by assuming (1) that accelera- 

 tion can be neglected and (2) that frictional forces can be neglected. On 

 these assumptions the components of the horizontal velocities are 

 obtained : 



10 dp , 10 dp .^.j ,». 



or 



«^x = V g^P.y and Vy = - - gip,x. (VI, 13) 



