Pacific Ocean Circulation — HiDAKA 
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ti cos dir = - r * (x ’ y) - ~ 1)2 T u ( x y) 
h f o df 2 2 h r /j A, W u ^ x <y> 
and (9) becomes 
d u 
dz 2 
Similarly we have 
tA U 
2 2 
(x, y) (2s - 1) 7 r 
4/j 2 
« s (x, y) r cos 
(25 — 1) TTZ 
2h~ 
~2 GO 
d zi 
dz 2 \h A 
v-v ; 2 T y (x, y) 125 — l) 2 7r 2 , . ( (25 — 1) tt 2 
= Z It - j V zz - - — 7^2 — ».(*. y) r cos - 
4/^ 2 
2 h 
where 
V' / \ (2^ — 1) TTZ 
= 2^ v s (x, y) cos . 
Substitutions of (7), (10), (11), and (12) into (6) and (5) give 
( d 3 u s 
_ dV\ 
125 — l) 2 TV 2 A z 
( du s 
_ dvA 
Vdy 3 
dx 3 / 
4h 2 
Vdy": 
dx / 
+ 
Mil His) _ o 
h \dy dx ) 
where R is the radius of the earth, and 
du s . d%h = 
dx dy 
Equation (14) gives a set of functions \ p s (x, y) such that 
and (13) becomes 
) 
dips d\p s 
u s = — ; v s = — — 
dy dx 
a i ti | tii) (P - i) 
‘ v dx* ~ r dy 4 / 4/z 2 
jtAi (tii + tii) _ 
V dx 2 dy 2 / 
dfy s dfy* ^ 0 cos (f> d\p 
1 - 2up -JTTx 
2 
+ 
/drx _ drA 
h Vdy dx / 
1 0. 
If we introduce two quantities Di and D z such that 
£T, 
v™ 
Di = 
and 
D z = 7 rJ-, 
\ pa> 
equation (16) becomes 
dV \ _ (25 — l) 2 / dA 2 / dfy s dfyA _ cos0 d\p 
27 r 2 \ dx 4 dy 4 / 8 \ h / \ dx 2 dy 2 / R dx 
dx 
+ 7 - (iin 
po)h \dy dx / 
( 10 ) 
( 11 ) 
( 12 ) 
(13) 
(14) 
(15) 
(16) 
(17 
(18) 
( 19 ) 
