Pacific Ocean Circulation — Hid AKA 
185 
direction. Neumann also expressed recently (1952) his opinion as to the necessity of a 
dynamic treatment of ocean currents as a three-dimensional problem. 
All these circumstances lead one to recompute the general circulation of the Pacific 
Ocean under these modified conditions and assumptions. The present investigation is one 
of the results of the author’s efforts in this direction. We here treat the general circulation 
of the water in a square ocean comparable in size to the entire Pacific Ocean basin. 
Spherical co-ordinates, which were used in a preceding paper (Hidaka, 1951), are not 
used here, partly in order to avoid mathematical difficulties but mostly because the two 
systems of co-ordinates did not give any important difference between Munk’s and the 
author’s results except for the magnitude of mass transport. The value of the lateral 
mixing coefficient is taken as 3.08 X 10 7 c.g.s., a value consistent with the research of 
former investigators. The wind system is considered zonal, because this assumption is 
far simpler for the subsequent analysis, and also because no essential difference has been 
found between the results obtained under the assumptions of zonal and anticyclonic wind 
distributions. Of course, the variation of the Coriolis parameter with latitude is taken 
into account. The use of current velocity in place of mass transport makes the mathe- 
matical analysis many times more complicated because the problem is now three dimen- 
sional. But the result will be of importance because it should give an idea of the vertical 
structure of the wind-driven circulation of the oceans. 
THEORY 
The dynamic equations of the stationary ocean currents, taking both vertical and 
horizontal mixing into account and neglecting the nonlinear terms, are 
a d 2 u d 
Al dy 2 + dz 
A d 2 v d 
1 dx 2 dz 
( A ‘S) 
— ) + 2u3 sin 4>pv 
(4h 
dp 
dx 
dp 
= 0 , 
(1) 
2« sin 4>pu — ~ = 0 
dy 
where u and v are components of the current velocity in x (eastward positive) and y 
(northward positive) directions, p is the pressure, p the density, Ai and A z the horizontal 
and vertical coefficients of eddy viscosity of the water, co the angular velocity of the earth, 
and <f) the geographical latitude. The axis of 2 is taken positive downward, the origin 
being placed on the undisturbed sea level. 
The boundary conditions to be satisfied on the surface (z = 0) and at the bottom 
(z = h ) are 
2 = 0: -A, || = t x (x, y): = T »(.h V) ( 2 
and 
z = h: u = v = 0. (3) 
Here both coefficients of eddy viscosity are supposed to be constants. The conditions to 
be satisfied along the coasts are also necessary. These are simply that there is no water 
flow across and along these coasts. If the coasts consist of vertical cliffs, we have 
at the shore lines. 
u = v = 0 
(4) 
