Ocean Currents in a Non-homogeneous Ocean 



487 



masses at the upper level move with an average velocity ^o and those at the lower level 

 with an average velocity Dj at right angles to the section. After unit time the water 

 elements, initially at AB, will lie at the line A'B' and those from the isobaric interval 

 CD at CD'. The total surface ABCD transforms into A'B' CD'. The change of the 

 projection of the surface ABCD on the sea surface thus becomes A'B'C'D", so that 

 ciF^ldt = {vq — v^L, where L is the distance between the two stations A and B. 

 Equation (XV. 11) combined with (X.45) gives 



{Vo = t'l) = 



Da- Di 



fL 



(XV. 12) 



This equation, which was first derived by Helland-Hansen (1905), forms the 

 fundamental equation of dynamic oceanography. From the difference in dynamic 

 depth of the isobaric surfaces Da — DbS. simple calculation gives the increase in velocity 

 from one surface to the next. Analogous treatment to that on p. 466, however, affords 

 only velocity differences and only the component at right angles to the selected section 

 is obtained. Equation (XV. 12) contains fundamentally the same as equation (XV.7) 

 derived directly from the equations of motion. In the practical appUcation of (XV. 12) 

 it should be noted that /)„ — Di, has to be expressed in units of the potential, that is, 

 in dynamic decimetres when the metre is taken as the length unit. The difference in 

 dynamic depth anomaly, e^ — €{,, can, of course, be used instead of the difference 

 Da - D,. 



The section to the south of the Newfoundland Banks between stations 205 and 206 

 can be used again as an example (see Fig. 202). Table 135 contains the dynamic depths, 

 their anomalies and values of €„ — ^6 for selected pressure surfaces down to 750 

 decibars. In equation (XV.12) <^ = 41° 10' N.;/= 9-60 x 10-^; L = 59 km and the 

 denominator is 5-664. The anomaly differences are multiplied by 10 in order to obtain 

 dynamic dm ; this gives then v in m/sec. The last column gives velocities on the assump- 

 tion that there is no motion at 750 m (see Table 133). If calculations of this type are 

 available for a sufficient number of station pairs it is possible to obtain a complete 

 velocity field at right angles to the cross-section. A comparison of the velocities cal- 

 culated in this way from the mass field with the observed velocities was first given by 

 WiJST (1924) for a cross-section through the Gulf Stream in the Florida Strait. The 



Table 135. Computation of the velocity profile south of the Great Banks of 



Newfoundland. 



