Appendix II. 



A Numerical Example 



Based on equations (35a, b), velocity profiles are determined for the meridional and 

 zonal sections defined by oceanographic stations 29, 32. 59, and 63, September 1961. 



The first step in the determination is to extract the geostrophic mode of transport 

 for the section of interest. This transport is included in equations (35a, b) as the first 

 and last terms in the numerator on the right side. Values of the total transport function 

 along the meridians of interest were plotted against latitude (fig. 64). The stations are 

 indicated on the plots of t//, and the total transport through the sections between the indi- 

 cated stations is taken by difference: 



Section 



63-59 



29-32 



63-29 



59-32 



(</><*„- </»*„) = [ -137-(- 112)] • 10 5 = -250 ■ 10 4 metric tons/sec 



(<//<*,„ -i/>,i> a ) = [- 192 -(-113)] • 10 5 = -790 • 10 4 metric tons/sec 



(<K-»K a ) = [-113-(-112)] • 10 5 = - 10- 10 4 metric tons/sec 



W»x„-<K a ) = [-192-(-137)] • 10 5 = -550 • 10 4 metric tons/sec 



It can be seen that continuity requirements for the total flow are satisfied by the results 

 of this procedure. Plots of zonal and meridional Ekman transport along meridians and 

 parallels are shown as figures 65, 66, and 67. Again the stations are indicated on the plots: 

 summations to obtain Ekman transport through the sections are performed using Simpson's 

 rule, or the trapezoid rule: 



Section 

 63-59 



29-32 



lU E Rd4>- 



2U E Rd<f) = 



98(2+12 + 4) , 142(4 + 36+15)" 



10 



= 3.2 • 10 4 metric tons/sec 



190(8.5 + 44 + 9.5) 52(9.5 + 34 + 8) 

 3 3 



• 10 



= 4.8 • 10 4 metric tons/ sec 



63-29 2V E R cos <j)dk ■- 

 59-32 XV E R cos 4>d\ ■■ 



344(18 + 94 + 36.5) 463(36.5 + 210 + 58.5) 



10 



64.1 • 10 4 metric tons/sec 



1520(2 + (-2.2)) 



10 



= —0.2 • 10 4 metric tons/sec 



The wind-driven geostrophic transport for a given section is the difference between the 

 total and Ekman transports: 



Section 



63-59 = (-250-3.2) . 10 4 =-253 • 10 4 metric tons/sec 

 29-32 = ( - 790 - 4.8) • 10 4 = - 795 • 10 4 metric tons/sec 

 63-29 = (-10-64.1) • 10 4 =- 74 • 10 4 metric tons/sec 

 59-32 =(-550 -(-0.2))- 10 4 --550 • 10 4 metric tons/sec 



Because the distribution of horizontal velocities is not highly sensitive to this geostropnic 

 transport, values for it can be extracted directly from tabulations of the geostrophic 



27 



