Figure 6. Force diagram of a non-accelerated gradient 

 current with friction. 



where R is the vector of the internal frictional force. For a 

 geostrophic current without friction, 



(24) 



On substituting (24) into (23), we have 



(M - M) x f = R . (2?) 



o 



Thus, the vector of internal friction is perpendicular to the 



1 -» -> 

 - - grad p + M„ x f = 



P y g 



difference vector M - M, and only in exceptional cases is p equal 



to zero. 



I ~* I 

 Suppose a is known, then p and IR I = R can be computed. In 



equation (8), for the components of the effective internal friction, 



we used for a first approximation Guldberg-Mohn's expression 



R x = - rU 



R y = - rV , 

 by assuming R = - rM. As in figure 6, let G be the vector of the 



32 



