480 



Ocean Currents in a Non-homogeneous Ocean 



If the isosteres slope downwards {upwards) from left to right when facing downstream, 

 then a steady current will show a decrease {increase) in velocity with depth {Northern 

 Hemisphere). 



It can be seen that equation (XV.6) allows a determination only of the vertical 

 velocity differences and it does not give the velocity itself and thus affords only relative 

 velocity difference distributions in vertical direction. This state of affairs recurs in all 

 similar cases and is a consequence of the indeterminate nature of the problem. 

 Equation (XV.6) has been derived from the equations of motion alone; to determine 

 the entire state of motion completely requires the continuity equation. Only then are 

 the conditions uniquely defined. 



Equation (XV.5) can be written also in another form: 



dv 



da 



oz cz 



gda 



fdx 



This can be used for a step-wise calculation of the vertical velocity distribution from 

 layer to layer (Defant, 1929 b). 



If at two stations separated by a distance L at a depth r = the specific volumes are 

 tto and a'o and at a depth z = h a-^ and a'^, the following formula can be used for a 

 numerical determination of the velocity difference ^o ~ ^i 



gh 



(ai + a'i)ro — (tto + a'o)fi = j^ {a^ 



a'o + «i — a'l)- 



(XV.7) 



Table 133 contains the specific volumes at six depths down to 750 m for the stations 

 205 and 206 on the section through the Gulf Stream and the Labrador Current south 

 of the Newfoundland Banks (Fig. 202). For = 40° 10' and L = 59 km the equation 

 (XV.7) gives the vertical velocity on the assumption of no motion at a depth of 750 m. 



Table 135. Calculation of the vertical velocity in the Gulf Stream south 

 of the Newfoundland Banks 



Werenskjold (1935, 1937) has developed a simple and practical method for the 

 same objective. Neglecting in equation (XV.6) tan ^ in comparison with tan y = /, 



