THE GNIRAL CIRCUIA1'TON IN THE NORTH PACIFIC
OCEAN REFERRED TO A VARIABLE REFERENCE SURFACE
by
WILLIAM BRUCE MCALISTER
A THESIS
submitted to
OREGON STATE UNIVERSITY
in partial fulfillment of
the requirements for the
degree of
DOCTOR OF PHILOSOPHY
June 1962
APPROVED:
Redacted for privacy
Prof es(or of Oceanography
In Charge of Major
Redacted for privacy
Chairmar(of Department of Oceanography
Redacted for privacy
Chairman of Scho&"Graduate Committee
Redacted for privacy
Dean of Graduate School
Date thesis is presented
Typed by Betty J. Thornton
May 18, 1962
THE GENERAL CIRCULATION IN THE NORTH PACIFIC
OCEAN REFERRED TO A VARIABLE REFERENCE SURFACE
by
William Bruce McAlistar
TABLE OF CONTENTS
Introduction .....................................................
1
The General Circulation in the North Pacific ................
3
Theoretical Studies of the Ocean Circulation ................
12
Methods of Current Measurement ...............................
17
Reference Levels .............................................
19
Theory...........................................................
21
The Determination of the Depth of No Net Motion ..............
21
Equations of Motion and Continuity
..........................
21
Geostrophic Currents ........................................
23
Wind-driven Currents ........................................
25
Total Transport Equations
...................................
28
Evaluation of Reference Depths ..............................
29
Sources of Data ..................................................
30
General.....................................................
30
The Surface Data ............................................
30
The Deep Data ...............................................
32
Wind Stress and Wind Transport ..............................
32
Geostrophic Transport .......................................
3k
Discussion of Results
............................................
37
ReferenceLevels .............................................
37
The Deep Circulation
Li-5
The Surface Circulation .....................................
Surnary..........................................................
5L
Bibliography.....................................................
55
Appendix.........................................................
59
Sources of Surface Data .....................................
60
Sources of Deep Station Data ................................
61
List of Symbols .............................................
62
Mathematical Derivations ....................................
63
TABLES
1.
Transport at Selected Sections in the North Pacific ..........
FIGURES
Fig.
1.
Circulation and transport in the North Pacific
(Sverdrup) .................................................
2.
Average dynamic height anomay in the North Pacific (Reid)
5
3.
1958 dynamic height anomaly in the Noith Pacific .............
6
4.
Circulation in the North Pacific (Hirano) ....................
7
5.
Deep circulation in the North Pacific (Sverdrup) .............
10
6.
Deep circulation in the North Pacific;7(Stommel) ..............
11
7.
Theoretical circulation in the North Pacific (Munic) ..........
15
8.
Theoretical circulation in the Subarctic Pacific (Hirano)....
16
9.
Station positions, 1958 ......................................
31
10.
Deep station positions .......................................
33
11.
Wind transport, Summer 1958 ..................................
35
12.
Volume transport, Summer 1958 ................................
36
13.
Difference of dynamic height along 140°W .....................
38
14.
Difference of dynamic height along 160°W ......................
39
15.
Difference of dynamic height along l75°W ......................
40
16.
Difference of dynamic height along l65°E .....................
41
17.
Difference of dynamic height along 36°N ......................
42
18.
Differences of dynamic height along 48°N .....................
43
19.
Differences of dynamic height along 40°N .....................
'-1-4
20.
Sections for computed transport ..............................
46
21.
Salinity
) distribution along 175°W longitude ..............
49
22.
Temperature (°C) distribution along l65°E longitude ..........
50
23.
Salinity 'i) distribution along 165°E longitude ..............
51
24..
Temperature (°C) distribution along l75°W longitude ..........
52
THE GENERAL CIRCULATION IN THE NORTH PACIFIC
CCEAN REFEREED TO A VARIABLE REFERENCE SURFACE
INlODUCTIC
One of the fundamental and enduring problems of oceanography has
been to describe the ocean currents and their causes.
Robinson and
Stommel (1959) refer to an exchange of letters in NATURE during the
1870's on the question of whether the wind stresses or the thermally
produced differences of density are the predominant cause of oceanic
circulation.
The nature and cause of the circulation of the oceans
remains one of the major problems of oceanography today.
The reason for our lack of knowledge is readily understood.
Direct measurement of steady-state suif ace currents is difficult.
Direct measurement of interior velocities and transports is very
difficult.
In fact, there are almost no unequivocal surface or interior
current measurements for the entire Pacific Ocean.
Current velocities
and transports are either estimated from the observed distribution of
physical properties, or inferred from solutions of the hydrodynamical
equations.
The most widely accepted patterns for the circulation come
from solutions to the hydrodynamical equations--solutions usually
derived under very restrictive hypotheses.
In the absence of con-
firming or refuting data, this method has poduced many hypotheses, but
little agreement.
During ninety years of sea-going investigation, it
has been possible to establish only the general configuration of the
surface currents and estimates or order of magnitude for the total
2
transport in some of the narrow, strong, and relatively well defined
cuorerts
as the Kuroshio and the Gulf Stream.
The only available
crHarion for testing, a new theory of ocean circulation has been that
it must esseotcaily reproduce the surface currents and the known mass
transport.
It has become apparent (28, p. 295-308) that by proper
choice of empirical constants many widely varying and physically
incompatible theories of oceanic circulation can be made to satisfy the
surface circulation.
As Stommel comments in the concluding paragraph,
p. 178, of his book, The Gulf Scream:
"1 should like to make it clear, finally, that I am not
belittling the survey type of oceanography, nor even purely
theoretical speculation.
I am pleading that more attention be
given to a difficult middle ground: the testing of hypotheses.
I have not explored this middle ground very thoroughly, and the
few examples given in this book may not even be the important
ones; but perhaps they are illustrative of the point of view
in which attention is directed not toward a purely descriptive
art, nor toward analytical refinements of idealized oceans,
but toward an understanding of the physical processes which
control the hydrodynamics of oceanic circulation.
Too much of
the theory of oceanography has depended upon purely hypothetical
physical processes. Many of the hypotheses suggested have a
peculiar dreamlike quality, and it behooves us to submit them
to special scrutiny and to test them by observation."
This study is an attempt to provide, from the available observational hydrogrophic data, estimates of the interior transport and
current fields in the North Pacific Ocean, and to compare these transport and current fields with those resulting from various theoretical
studies.
Since no direct observations for currents in the North Pacific
are available, the current fields used in this study have necessarily
been derived from consideration of the hydrodynamical equations, but in
such a manner as to make the current fields relatively independent of
the assumpticns involved.
The current and transport fields thus
3
obtained must be consistent with the observed distribution of properties
and general circulation in the North Pacific Ocean.
The General Circulation in the North Pacific
Virtually all descriptions of the Pacific Circulation have been
based on. the observed distribution of physical properties and assumed
geostrophic flow.
A summary of the general circulation in the North
Pacific is given by Sverdrup et al. (38, p. 712-728).
The circulation
and volume transport according to Sverdrup is summarized in Figure 1.
Since this study is largely restricted to regions north of 4O°N, it is
necessary to examine some of the more detailed descriptions of this
region.
The. North Pacific, virtually unexplored before 1940, has been
investigated in a fairly extensive manner during the last decade.
Descriptions of the circulation of the surface layers of the Pacific
north of 30°N have been given by Bennett (1, p. 565-633), Hirano (15,
p. 11-39), Reid (27, p. 489-502), Tully (42, p. 91-112), Doe (9,
p. 1-34) and Dodimead and Favorite (8, p. 1-46) among others.
Figure 2
shows the average anomaly of the geopotential depth from the surface to
1000 decibars (27, p. 491).
Figure 3 shows the surface to 1200 decibar
anomaly for the year 1958, which will be used in this paper.
Figure 4
shows a general schematic pattern for the North Pacific circulation
given by Hirano (15, p. 12).
All the patterns show broad agreement.
The main features of the observed circulation are:
the crowded
0
isolines indicating strong surface currents at latitude 35°N, longitude
145E showing the main axis of the Kuroshio; the intrusion of water
1400
IG°
50°
1700
70°
1500
lE0°
I10°
I20
-
CS0
/
c (
-:
-
-
-
I
-
.-:.
-
kk; -
-
60°
L"i9±I
It.
:
/
1,_I:4
/
//
ç!í-
/
55°
_i
g:.
I
I
J
(
II
I
°'. :°
/
I
N
V
r
j
/
- '5 -
/1
/
430
2
430
_; H
I
53,
45°
:
-
)'-
to
-
/
20
I
300
5
)
-.
_7
25°
t
400
30°
153°
FIGURE 1.
50
-:
-I-
700
800
_t::700
1000
IO°
140°
GircuJation and transport in thc North Pacific (Sverdrup).
130°
25
120°
y
/N
ii
:'
I
-
4Q0
35
.2
1
)
j
'
40
I 4
/
-.
L5
I6
\
30
NI
22
25
1400
1500
FIGURE 2.
350
300
250
1600
1700
1800
170°
60°
500
140°
1300
120°
Average dynamic height anomaly in the Forth Pacific (Reid).
Lfl
lir
170
I/o
&
NOTH PACIHC
DYNAMIC HIIIT
-
.' Y (f
2
0/1200 rCI
CONYUU
IN
..
I...:.
-ç
Set.
B
:-,'
--
4
U
;
---- L3 - -- -
-
5_-
l--
LcS
____________
FIGURE 3.
1958 dynamic height anomaly in the Eorth Pacific.
L5
2
0
3Q0
300
2 5
250
1400
1500
(60°
FIGURE 4.
(70°
(800
700
(60°
(5Q0
Circulation in the North Pacific (llirano).
(400
L0°
(200
from the Okotsk Sea at latitude k5°N, longitude 150°E, and the general
counterclockwise flw in the Gulf of Alaska out along the Aleutian
Islands end into the FerLng Sea.
Tireno (IS, p. 12) has associated water masses with the three
semi-permanent
gyros shown in Figure
-.
Thu
elativu permanence of
the water in these three gyres allows the water to assume distinctive
characteristics.
A strong front, separating the Subarctic Pacific
Water from the Pacific Central Water exists along the southern boundary
of these gyres.
Relatively little information, even by inference from water
properties, is available for the deeper layers.
The state of knowledge
as summarized by Sverdrup (38, p. 751-755) remains almost unchanged.
Deep and bottom waters of high density are formed only in high
latitudes.
Formation of deep water does not occur in the North Pacific
because of low surface salinities and limited exposure to polar conditions.
It is generally accepted that the Pacific bottom water orig-
inates in the Atlantic Antarctic (6, p. lL9).
Pacific basin south of Tasmania.
This water enters the
Recent carbon-l'-l- measurements in this
region (2, p. 107-108) suggest that the entering waters are already
several thousand years old, but. the published observations are not
conclusive.
Some fraction of the Antarctic bottom water flows northward into
the southern and central basins.
Sverdrup has suggested that a
sluggish northward flow takes place on the western side of the South
Pacific Ocean with return flow to the south on the eastern side.
exchange of deep and bottom w.
The
r across the equator is believed to be
very small.
The average velocities of flow have been estimated as
fractions of a centimeter per second.
According to Sverdrup, deep
circulation in the North Pacific Ocean is a general northward flow
(Pigure 5).
In a recent paper, Stommel (33, P. 85-90) has described a
theoretical model of the abyssal circulation.
Stommel envisions a
balance between two "point sources" of deep water (in the North
Atlantic and the Weddell Sea) and an oceanwide "sink" with upward
flux
everywhere across the two-kilometer surface.
If the sources are
connected with this distributed sink in a way consistent with
the
dynamics of a fluid on a rotating sphere, it appears that
the
meridional component of velocity in the deep sea is everywhere directed
away from the equator, where it vanishes, except in the western
parts
of oceans, where intense boundary currents occur.
In the western
Pacific, a strong current flowing northward across the
equator toward
the 30°N parallel is suggested; north of it there is
an oppositely
directed boundary current.
A schematic diagram for the North Pacific is shown in Figure
6
(33, p. 85-90).
Wooster and Volkman (L4L1, p. l239-l2'49) discuss the abyssal
circulation of the Pacific Ocean in reference to the distribution
of
properties at 5000 in.
Their conclusion is:
"In the northern basin changes in the properties of
bottom water are smaller, and the nature of the circulation
is not clear.
The slight west-to-east increase in temperature
across the North Pacific is compatible with the classical
picture of clockwise circulation, as is shown by the
arbitrary
flow line. A slight decrease in
oxygen content (and an increase
50
350
30°
300
25°
250 :==
140°
150°
160°
FIGURE 5.
1700
1000
170°
160°
50°
400
IJ
120°
Deep circulaLion in the. Uorth Pacific
C)
I.
II
/
r'
I " p' -:i:T---,
40
3O
250
1400
1500
600
FIGURE 6.
170°
800
70°
600
50°
140°
Deep circulation in the North Pacific (Stommel).
300
1200
12
in that of inorganic phosphorus) is also consistent with the
indicated direction of flow.
On the other hand, temperature
data from the eastern basin suggest that waters there are
derived from the central basin, rather than from the eastern
part o: the northern asin, In either case, it seems likely
thst bottom water of the eastern North Pacific, with the
highest temperature and lowest oxygen concentration, is the
oott . a "r of
te oy Pc. ifte
Thus, we find the present data inadequate to offer much support
or opposition to theories of the abyssal circulation.
Theoretical Studies of the Ocean Circulation
As has been indicated, theories of the ocean circulation form
roughly two groups, depending upon whether they presuppose wind stress
or thermohaline effects as the driving force of the ocean circulation.
Both models have been proposed for the North Pacific circulation.
It
may be useful to summarize briefly the various stages of development
of the wind-driven theories.
The first successful development of a theory of wind-induced
currents was that of V. W Ekman (33, p. 493).
Ekrnan obtained
solutions for surface wind drift in the presence of only an eastern
boundary and uniform wind stress.
This drift current is limited to
the surface layer; significant transport rarely is found bneath 100 m.
Ekman gave a qualitative argument that in the presence of boundaries
and non-uniform wind stress the wind-induced currents will extend much
deeper.
The difficulties of an analytical solution to the hydrodymical
equations directly for the current field in the presence of boundaries
remain unsurmounted, however, after more than 50 years.
13
A tochriciva of Lntegrating the equations of motion over the
depth, which avoids tiauy of the nu-shematical difficulties, was
davelceed by Shtokman (32, p. LC3LO6).
n this method, only net mass
transoorts and no vertical veioc:t.y profiles are obtained.
Successful
application of this method has resulted in a series of valuable studies,
Using this method, Sverdrup (39, p. 318-326) showed that in an
ocean of constant depth bounded only on the east, the meridional mass
transport in the absence of friction depends on the curl of the windstress and the variation of the Coriolis parameter.
The simplest, and perhaps most basic, model in the theory of the
wind-driven ocean circulation is that of Stommel (37, 202-206), which
first offered an explanation for the westward intensification of the
currents.
Stommel considered a rectangular homogeneous ocean of
constant depth, and a simple form of wind stress, varying sinusoidally
with latitude.
Munk (19, p. 158-167) used actual wind stress data, and included
a more elaborate and theoretical treatment of internal friction.
He
also considered basins with shapes approximating the real oceans.
The
resultant current patterns are so strikingly similar to the observed
surface circulation that it has been taken as a strong argument for
the hypothesis that the ocean currents are primarily wind driven.
Morgan (18, p. 301-320) and Charnay (Li., p. LI.77_Ll98) have extended
the theories of Stommel and Munk by including additional terms.
A
solution similar to Munk's (19, p. 158-167) was obtained by Hidaka
(lLi, p. 183-220) with the same assumptions but different expressions
for the friction and the wind stress.
Neumann (21, p. 1-33) has
lL-
pointed out that the latitudinal variation of the. depth of no motion
can have an effect similar to that produced by the variation of the
Coriolis paranetar.
Transport streamlines for a triangular North
Pacific Ccean as obtained by Munk, are shown in Figure 7.
Hirano
(15, p. 11-39) has adapted Storrmei's and Morgan's models for various
wind stress systems in the Subarctic Pacific.
The streamline pattern
for Stommel's model (37, p. 202-206) with a particular choice of wind
stress is shown in Figure 8.
Hassan (13, p. 36-43) has treated the problem by sloping the
depth of no net motion latitudinally.
The papers by Hidaka (14, p. 183-220) and Hassan (13, p. 36-43)
are of particular interest in that they attempt to determine not only
the mass transport, but also the vertical velocity profiles.
Hidaka's
solution has indicated a surface pattern of flow similar to that
previously found for the mass transport.
At subsurface- depths, the
pattern of flow does not change greatly from that at the surface, the
velocity falling off comarative1y slowly with depth.
Hassan's pro-
files are more complicated and require a two-layered system in the
oceans.
Features of these theoretical eiru1ations will be examined
in more detail and compared with the flow field obtained in this
study.
A thermohaline model for the Pacific has been suggested by
Robinson and Stommel (28, p. 306) .
The most interesting feature of
their model is perhaps the slow upward component of velocity present
everywhere in the deep water.
The structure of the model is too
/
FIGURE 7.
Theoretical circulation in the North Pacific (Munk).
I
--
FIGURE 8.
--
Theoretical circulation in thc Subarctic Pacific (ilirano).
17
general to permit confirmation.
However, it does imply certain
restrictions, mentioned previously, on the abyssal circulation.
Methccs of Current Measurement
Successful direct measurement of ocean currents is limited to
strong, well defined currents, with accurate position control.
Various
schemes of direct measurement of ocean currents have been attempted
using different types of current meters from anchor positions.
It has
been difficult, however, to eliminate two sources of systematic error.
The ship may surge or move on the anchor line due to shifting currents
or winds at the surface.
Pickard (2k, p
635-678) has shown that even
in the restricted environments of an estuary this can lead to erroneous
current measurements unless a very careful record of the ship's
position is available.
available at sea.
This required positional accuracy is not
Measurements from anchored ships and buoys will be
strongly affected by tidal action as well,
in general, tidal currents,
even near the bottom in the deeper parts of the ocean are greater in
magnitudethan the mean circulation (k3, p. 1-38).
Thus, in the
absence of supporting data, individual current measurements are almost
meaningiess to define mean circulations.
One method of avoiding these
tidal and positional difficulties is to employ average values by taking
serial measurements over a long period.
However, serial measurements
over periods long enough to eliminate the periodic and some non-
periodic variations still must contend with cumulative effects of wind
and drag and are still generally unreliable (7, 506-519).
The only
18
succes:ul duep sea current observation from an anchor station appears
to be the "Altair' s ation from the METEOR Expedition reported by A.
Defont (5, p. 19t-2fC).
MFnV of the same comments apPly to current
valuer. from drcgues mad drift bottles.
Locating a drift bottle tells
little about the trajectory and velocity of the bottle
In recent years, new techniques of deep current measurement, such
as the neutrally buoyant Swallow floats, have been introduced (Li.O,
p. 7L_81)
(L.1, p. ll83_1l8L.).
The early results, all from the Atlantic,
shov high variability and low reproducibility.
High cost, both in
in:itial investment and tracking time, presently limits extensive use of
the Swallow floats.
The one classic example of useful and unequivocal
direct measurement of ocean currents remains Pillsbury's measurements
in the Straits of Florida made between 1885 and 1889 (38, p. 671i).
Indirect methods relating the circulation to the observed physical
properties have been used for more than eighty years, since the first
CHALLENGER Expedition. A typical technique is to associate a tongue of
certain properties with currents.
This method has been used with some
success by Montgomery in explaining the South Equatorial Current in the
Atlantic (17, p. 2k2-250), where he used horizontal salinity profiles,
and by H. R. Seiwell (30, p. 1-86) in offering a description of the
deep currents in the eastern North Atlantic on the basis of oxygen
distribution.
The indirect methods are always subject to strong
reservations and possibilities of alternate explanation, and usually
involve rather arbitrary values of diffusion and turbulent coefficients.
Application of the hydrodynamical ecuations has produced the most
extensive and valuable informaton on the steady currents in the ocean.
19
The CUrrCn;S which cecur when the geostrophic mass-accelerations are
equvalant to the forces derived from the pressure gradients are called
"feostrohtc" otr
nts.
Their imoortance lies In the fact that it is
posstbfe to dertve the gecstrophic current at the surface, relative to
that at any depth, In terms solely of the density structure of the
water to that depth.
This result, derived by Helland Hansen in 1903
(6, p. 487), opened a new era in oceanography, and has been the basis
of nost of our knowledge of ocean currents ever since.
The geestrophic eçuation, however, cannot provide knowledge of
transports or absolute velocities, since the geostrophic currents are
given only relative to the value at some reference depth.
By choosing
a reference depth at which the velocities are zero, surface velocities
relative to this depth become absolute values, but we usually have no
information as to what the depth is if in fact it exists at all.
In
the North Pacific, and for the oceans as a whole, it has been common to
take the reference depth as near 1000 m.
of exparience
This is basically a choice
made because most of the available measurements do not
reaco deeper, rather than because any special significance can be
attached to 1000 m.
Reiaree Levels
In much of the early work in oceanography, it was sufficient to
describe the surface currents, and to assume that the interior circulation resembled that of the surface;
The usual procedure to overcome
difficulties in the choice of a reference surface was to choose a very
deep level, or the deepest available measurements--commonly about
20
1000 rn--at which it is reasonable to assume that the velocities vanish,
or become very small compared to the surface velocities.
While surface
velocities are relatively insensitive to the choice of a reference
sun' a
transport properties are very strongly affected (7, p. 506-519)
deia:u (, p. liil-230) has givcri an intuitive criterion for
determining a depth of no net motion, locating it at that level at
which the vertical gradient of the geostrophic velocity vanishes.
This was based on a comparison of water properties and geostrophic
velocities in the Central Atlantic.
Ostapoff (23, p. 1-31) has extended
this method to the Central Pacific.
While the single reference level
determined by Ostapoff is not directly comparable to the separate zonal
and meridional reference levels determined in this study, both agree in
showing lower reference levels to the north.
During the last ten years, many of the advances in our
understanding of the oceanic circulation have come through use of the
vorticity equation to provide integrated transports.
By appropriate
integration of the equations of motion, it is possible to establish
transport values independently, and by comparison with the geostrophic
transport to locate a reference depth, and to determine absolute'
currents and circulations.
Implicit in th
method, however, are some
not very explicit restrictions and assumptions about the reference
level.
One of the purposes of this paper is to examine the extent and
depth of the reference surface in the North Pacific, and implications
of the variation in depth of the reference surface, zonally and
meridionally upon the dynamics of the circulation.
We find that the
21
reference surface is variable both zonally and meridionally, and that
at any given location the depths of no zonal motion, and of no
meridional notion &:.ra not coincident.
Reference levels may be defined
for zonal or n :idio:al flow; however, reference levels in the sense
used by Dietrich, Defant, Sverdrup, and others do not exist in the
North Pacific Ocean.
THE CRY
The Determination of the Depth of No Net Motion
Under certain general conditions it is possible to determine
the depth of no motion from hydrographic data at a pair of stations.
Total transport may be evaluated in terms of the curl of the wind
stress using any of the various theories of the wind-driven
circulation.
If for a given section, the value of the wind-stress
transport is taken as absolute transport, then it is possible to
choose a reference level such that the integrated geostrophic
transport just matches the transport computed from the wind stress.
A procedure 'using this method to obtain the depth of the reference
leiels from available data will be derived.
Some subsidiary
relations in discussing the application of the various theories of
circoThtion to the North Pacific Ocean will also be derived.
Equations of Motion and Continuity
The steady state time-depenant equations of motion are:
22
(1)
(2)
-
) "Pa
-
(3)
____
nO
(Li.)
Terms which are small compared to the scales of motion considered
in the general circulation of the ocean have been neglected.
horizontal component of the coriolis force,
neglected in (1) and the vertical component,
neglected in (3).
-2icos w
,
The
has been
2cos u ,,has been
Vertical accelerations and frictional forces
have been neglected in (3), and constant eddy viscosities (AH, AV)
have been substituted for the Reynold's stresses.
The equations
are, however, valid for a discussion of oceanic circulation
(25, p. 50, p. 97)
A list of symbols is included in the appendix.
Complete
derivations of the equations have also been included in the appendix.
Only that part of each derivation pertinent to the discussion at
hand has been included in the text.
23
Caotrot
C>irrents
a regica vhf: a tha a are no strcng velocity gradients, nor
fctiaaal fcrces, acatica
t
-ai.ont
7
1) and (2) express the balance of
sure grad ........ and the C:riolis forces.
The
geostrophic equations are:
((5)
(6)
In terms of anomalies of geopotential,
or 'dy-namic heights,' the
velocity at any surface relative to the velocity at an isobaric
surface is given by:
(7)
Velocity differences omputed from (7) or its integrated form are
rcferred to as
lativ
:aostrophic velocities.
With regard to the development of equation (7), several points
should be kept in mind.
Since velocities are normally much smaller
at depth in the ocean than at the surface, the relative velocities
at the surface derived by use of ecaation (7) will be almost the
same whether referred to, for example, a 1000 m reference surface
or to a 2000 m or lower reference surface.
Thus, the dynamic
2'-
torography at the surface provides reasonable values of
surface
currents.
At ssma distance beneath the surface, usually not more
than savarel hundred caters, the vale of the relative
geostrophic
current drops to annrcximataly the same order of magnitude
as the
origral uncertainty in the current values at depth, and values of
interior current become indeterminate.
These small velocities,
when integrated over thousands of meters to the
ocean bottom, can
contribute to the total transport as much or more than the
high-
velocity surtace layer of limited depth contributes.
Thus, in the
absence of an ahsoThte reference surface, transport
values from
geostrophic currents are unreliable.
In th
deeper parts of the ocean, the isobaric surfaces tend
to become parallel.
That circulation which takes place when the
isobaric surfaces are parallel to the isosteric
surfaces is called
the barotropic circulation.
The barotropic velocity will be
uniform with depth and equal to the deep
water velocity.
The
circulation where the isobars are inclined
to isosteric surfaces
is called th
haroclinic circulation.
The baroclinic velocity then
will be given by the geostrophic current in the
baroclinic layer
relative to the deep water velocity.
25
Wind-driven Currents
By use of several general assumptions, it is possible to simplify
the general hydrodynamical equations for a wind-driven circulation.
Csorvaticns show that, away from the boundaries of the oceans,
accelerations are small, horizontal friction is small compared to
vertical friction, and vertical velocities are small compared to
horizontal velocities.
Ijnder these conditions, equations (1) and (2)
represent a balance between vertical friction, pressure gradients and
coriolis forces.
Under these assumptions dquations (1), (2) and ()
may be written:
-
7r
(8)
V
*
(9)
*
(10)
Equation (3) remains unchanged.
Bottom velocities are known to be small, and velocity gradients
near the bottom must be negligible.
Thus, the bottom stresses may be
neglected by comparison with the surface stresses.
utilized by integrating equations (8), (9)
,
This fact is
and (10) from the surface
to s3me depth at which the bottom stresses vanish.
This depth may
conveniantly be taken as an isobaric surface at the bottom.
26
A ccnvcnient notation is used for several of the terms appearing
in the integrated equations.
Comr,onents o
respeative.y the
mass transport
U
and
V
representing
ast-west and north-south cdmponents of the mass
transport per unit width from the bottom to the surface of the ocean
caused by wthd are defined by:
(11)
J
vJ
(12)
The pressure terms are first integrated by changing the depth
differential to a pressure differential.
Also, according to Leibnitz'
rule, an additional term will be introduced by the interchange of
differentiation and integration.
(13)
J
x
fl- +
1
!
(1k)
If the pressure surfaces are level surfaces, these additional
terms will vanish, and the following system of integrated equations
is obtained:
4
27
/bv
LuyLj
J
(15)
'?<1L11
--
(16)
0
(17)
Equation (15) is differentiated with respect to y, equation (16)
is differentiated with respect to x, and the two resulting equations
are added:
v
zp
P1
Substituting
-
we may write:
1/
/
/fl
Cqr/2
1,
The mass transport associated with the wind,
(18)
V
and
lJ
will include components associated both with the presence and with
the absence of pressure gradients.
That wnd-driven transport
which exists in the absence of a pressure gradient has been called
the Ekman transport.
The east-west and north-south components of
the Ekman transport are given by (6, vol. 1 p. 403):
(19)
(20)
We shall use the symbols
VS
and
for that part of the
wind-driven transport associatH with the presence of a pressure
gradient.
This transport
wil
Jso appear as part of the geostrophic
transport.
The Ekman transport is normally small compared to the
geostrorhic transport.
Lw =
V.
We may write:
1j3 + Un
=
(21)
e
(22)
Total Transport Equations
Fofonoff (11, p. 30-33) has shown that the total transport in
an interior region of the ocean is made up of three components:
the Ekman transport, the wind-driven baroclinic transport, and a
barotropic transport.
U
= US+UB+UE
(23)
V
= VS+VB+VE
(2k)
The barotropic transport appears due to the inclination of the
pressure surfaces at the bottom.
()
(I
(25)
P /P5
(26)
Both the baroclinic and barotropic transports will appear as
part of the geostrophic transport.
Ug
US+UB
(27)
Vg
VS + VB
(28)
29
Evaluation of Reference Depths
Iquaiori (7) end equericns (15) thru (28) have been evaluated
for the su. n.r of 158.
Using transport values computed from surface
winds for July and August, 1958 (12, p. 1-87), successive values of
VS
,
evaluated from equations (18), (20) and (22) have been
°
computed for
Values of
U5
intervals across the North Pacific, north of 36°N.
have been computed by integrating the values of
across the ocean, setting
US
equal to zero at the western and
eastern boundaries, and applying continuity to each successive section
in the grid (Figure 11).
The assumption is commonly made that the barotropic transport is
negligible.
This assumption, however, does not appear applicable to
the North Pacific.
The deflection of flow with respect to bottom
topography at L4.000 In in the western North Pacific, as inferred from
the distribution of properties (16, p. 99-110), implies a residual
barotropic transport at depth, roughly parallel to the bottom
contours.
The reference depths have been
in the various sections such that
valuated by selecting that depth
1J
and
Vg
will be the same
whether computed from equations (27) and (28), or computed from the
dynamic observations (equation 7).
30
SOURCES OF DATA
General
The data used fit into two sets.
One set was used to determine
properties from the surface to 1200 m.
This will include most of the
surface and subsurface layers, which are subject to seasonal influence.
The second set of data is from deep stations, and was used to determine
the hydrographic structure of the Pacific Ocean from a depth of 1200 m
to the bottom.
The Surface Data
All of the data used in stirface to 1200 m computations were
collected during the summer of 1958.
Oceanographic coverage by the
various independent agencies during this summer was one of the most
extensive ever attained
various stations used.
or the North Pacific.
Figure 9
shows the
Altogether, there are 505 stations in the North
Pacific occupied between late June and the end of August.
Most of the
stations extend to 1200 m, although some only extend to 1000 m.
data used in Figure
9 are listed in the appendix.
Much of the data
represent a cooperative survey of the International North Pacific
Fisheries Commission.
The
31
-'
ISO
60
760
l70
075
ISO
I/S
I/O
165
III
ISO
'0
45
II
NORTH PACIFIC OCEAN
Station
65
-
Positions
NM C S. 0570oo
S
Ryolu M0,u
0
Mv AOO
c N A V. Wh,61th,006
0
50,0 NOFu
S
MV P,onte.
A
M.V Key WesT
S
MV Fort Ross
HOSUNIT MOru
70
II
Oshoro MOrU
II
MV 0,006 800,
I)
MV NM SmVfl
SUMMER 958
6
.
V
U
FIGURE 9.
0
Station positions, 1958
32
Tha Deep Data
For the comnutational method used, the dynamic topography must be
rederred to the hotom.
During any given year, 195d being no exception,
little or no sampling below 2000 ci has been done over large regions
of
the North Pacific.
Thus, it has been necessary to devise a method of
extending the 1958 dta to the bottom.
Robinson (29, p. 2097-2116) has
shown that there is no indication that the properties of
specific water
masses, and the deep water in the North Pacific in particular,
are
undergoing systematic change.
Thus, it was assumed that the surface
stations could be extended to the bottom by use of
mean conditions in
the deep water.
Rattray (26, p. 1099-1107) has shown that, though
water mass characteristics
may not change, shifts in the transition
zone between subarctic and equatorial water may have occurred
during
the interval from 1929 to 1958, and these shifts
may affect the deep
water.
Accordingly, it was decided to limit the survey of deep
stations
to the time period within five years of 1958.
All available data from
the years 1953 to 1961 for the North Pacific
were plotted and averaged.
The number of deep stations used varied from 579 at 2000
ci to 82 at
LiQQ3 ci and 27 at 5000 ci.
The location of the stations used is shown in
Figure 10, anda complete list of the stations is included
in the
appendix.
Wind Stress and Wind Transoort
Fofonoff (12, p. 1-129) has calculated mean monthly
wind stresses
from mean sea level atmospheric pressures, and
published mean monthly
I50
160°
170°
190°
65
1700
)
160°
1500
1400
120°
'-S
65°
°°
coo
55°
550
M
500
/1
50°
/
10
45°
40°
35°
1
.
350
30°
.
30°
25°
140°
150°
160°
170°
1600
FIGURE 10.
170°
25°
160°
Deep station positions.
150°
140°
130°
120°
314
meridional transports for various years including 1958.
Since the
vcThme rransoort calculations were based upon data collected during
JL:Iy an: :ust 19i3, values of the geostrophic mass transports fc:
wo aonths ware awraçcd.
Internolated values were computed for
toe boundaries of L° scuares, and continuity across the ocean
obtnined.
Zonal and meridional comPonents of the wind transport used
in this study are shown in Figure
11.
Ceostrophic Transport
The information calculated from available data includes estimates
of geostrophic volume transport referred to standard reference surfaces.
These are of value in comparison with the total transport.
Since these
are surface transports, they reflect the high surface velocities, and
the patterns in general resemble the dynamic topography.
However, the
volume transport between individual stations shows some features not
readily apparent from the contoured fields of dynamic height topography.
Calculated volume transports during summer 1958 between selected
stations referred to 1200 rn are shown in Figure 22.
These may be
compared with the surface to 1200 ra dynamic height topography in
Figure 3.
In the summer of 1958, geostrophic transport in the Gulf of
Alaska gyre was calculated at 13 million m3/see referred to 1200 m,
which may be compared with the 17 million rn3/sec referred to 2000 rn
reported by Bennett for 1955 (1, p. 565-633).
Transports in the western Pacific are similar but not identical
to those reported by Sugiura (31, p. 81-85), which were referred to
1500 m.
140°
150°
150°
800
1(0°
70°
1500
IGO°
fr0O
-
_______
65°
6'
ffLnspor
J/
50 000
60°
55°
5°
233
232
3-- 5 ° .--
232-
)
40
500
134
230
69
110
f47191 S
132
iOfi
210
2I.
290
23,
207
250
43
67
15i
23
L-
123
-
S
-
-
°"-
2)
3
s
-
35°
/
750
Z12
-'4
2
7O1
2-.
15
217
'
235
21
230
55
214
51 IC
5
222
193
212
t
2)
5
101
169
1315 323
5
227
205
93
-9
166
193
44
3
63
r- 33
160
1
25y
145
19
60
f
9
3
f 2S
23
30
i3
60
1
1-
1
2
j.
21
7
19± 3'H
-;_
45°
2
?2
40°
?0
11+26122+7-f 1L :
47
50
25
7
I
I
0
7
Io
'-I
17
I
34+ 30T 50i 37
9 50
50°
I'
3?
3
71
30
526
29
10
Y 101
39
10
100
126
159
591
1
22,17H 33- 3S-.-3?U sH
235
?C
U
S+ 17
12
0 -;- 2o
2o9
2'-)
3
290
262
-.0
40°
SC
1
t
.'::,'-
So
94323f6ot3/5f9 ')32r
32
200
293
113
450
s-
41
2
-.
7122
12
257
275
213
1.
171
173
So)
14
3?
56
12 f
33
33
24
36
i
214
.9
1
-
1
3
30°
30°
250
i-i 25°
1400
1500
50°
170°
FIGURE 11.
ICO°
1700
150°
150°
140°
30°
120°
Wind transport, Sururncr 1958.
02
03
36
140
15O
180
170
i4O
15O
13O
106 M3 /SEC.
<0.5
x
+
0.5-2
i
2-4
4-6
6-8
i 8-10
= 0-20
20-30
-
N
4
/
+
4
4
'/
50
4
4-
4
*
.
4
--
*
/
.
.
0-
-.
I
b
__
/
\
4
40
1
140
i
150
160
Lo gtude 1 0 Last from Greenwch
i-1
180
FIGURE 12.
LolgI de 170 West I
0 e 1W CO
160
150
Geostrophtc volume transport, Summer 1958
14(1
130
37
Cor:tinuity o
transport gives a strong Aleutian boundary current.
Loss through toe Aleutian passes is not shown, but drift bottle
raeasurumuots reoi to indicate most o:: the nortoword fiow or about 11
mrll:ou r/seu must occur eastward of Attu.
Thrs flow, assuming only
a small loss through Bering Strait, is balanced by en equivalent
Oyashio intrusion along the Asian coast.
Superimposed upon the volume
transport chart (Figure 13) is the Pacific-Subarctic:Pacific-Central
Water boundary.
One interesting feature of the volume transport
is the presence of westward transport along this boundary.
DISCUSSION OF RESULTS
Reference Levels
Results of the computations are illustrated in Figures 13 through
19.
The curves represent the slope of the isobaric surface at their
respectivesections, and are proportional to the vertical velocity
profile (equation 7).
The sections across which the slopes are
computed are approximately 10° wide on the longitudinal profiles, and
L° wide on the latitudinal profiles.
Integrated transports have been
computed for each section from equations (7) and (18) (see
p. 29).
That depth which produces the best agreement between the two methods
is marked on each curve (+); this defines the depth of the reference
surface.
north.
In the longitudinal sections, the slope is downwards to the
The latitudinal sections appear to show a slope upwards to the
west, but the slope is not as well defined as in the longitudinal
sections.
0
1000
2000
3000
L.000
LJ
0.1 d. cm
5000 L
360 N
p40°
FIGURE 13.
L4°
148°
Difference of dynamic height along 140°W
52°
56°
1000
2000
3000
4000
.cm
5000
L.
36°N
440
400
FIGURE 14.
480
Difference of dynamic height along 160°W.
52°
56°
0
1000
2000
3000
14000
5000
36°N
400
4/40
FIGURE 15.
48°
52°
56°
Difference of dynamic height along 175°W.
.1:-
0
0
1000
2000
3000
4000
500C
oI
140
0
FIGURE 16.
Difference of dynamic height along 165°E,
0
1000
2000
3000
4000
0.1 d.cm
5000
150°E
160°E
FIGURE 17.
170°E
180°
Difference of dynamic height along 36°N
170°W
1000
2000
3000
4000
160°E
170°E
180
l68°W
150°W
138°W
1-
()
FIGURE 18.
Differences of dynamic height along 48°N
7 7Th1
10
20 0o
30 00-
40 00
50
______
I
150°E
160°E
170°E
LL_
180°
170°W
150°W
0.1 d.cm
135°W
.1::-
FIGURE 19.
4:-
Differences of dynamic height along 40°N
45
It does not appear possible to establish reference levels
at the
western boundary by this method.
The wind stress values, Figure 11,
increase up to this boundary, resulting in the
strong bourary flow
at the weetem boundary.
This f.ow actually extends eastw:rd, with
associated greater turbulence.
In this region, the assumptions for
equation 19 no longer are true, and the simplified
expression for the
transport can no longer be expected to hold.
A second anomalous region
appears in the section between 36°N and 40°N about mid-Pacific.
region shows a substantial
This
transport counter to the prevailing easterly
transport to the north and south.
This transport is observed, but
displaced several degrees to the south, and the
transport between 360
and 40°N appears uniformly easterly in
these longitudes.
The deep circulation
Although it would have been helpful to have
more deep stations,
enough are available to establish an
average transport over sufficiently large distances.
Using the observed reference level at
meridional transnort has been calculated
for sections above and below
the reference level from 145°E to l32°W,
divided at about l72°W.
sections are shown in Figure 20.
Results are given in Table
//
1.
The
V0c,
1600
1500
700
600
70°
60°
ISO"
40°
120°
C
60°
0
60°
0
55°
55°
:
500
'7
45°
:
40°
-
:
350
350
30°
30°
25° =
1400
5°
150°
00°
170°
FiGURE 20.
80°
170°
60°
150°
Sections for computed transport.
140°
1300
1200
L7
TABLE 1.
Section
Transport in 106m3/sec
Tpr Laer
A
Lower Layer
20
S
12
B
S
22
N
1k
C
E
28
W
10
In the western section, the level of no net motion is at about
1500 m.
Transport is to the north in the upper layer, and to the
south in the lower layer.
The transport in the 1ower layer is. of
the same order of magnitude as that in the upper layer, although
somewhat smaller.
In the eastern section, the level of no net motion is at about
1200 m.
Here. transport is to the south in the upper layer, and to
the north in the lower layers.
the western side of the Pacific.
side of the reference surface.
Both transports are greater than on
The flow does not balance on either
The additional northward flow at
depth in the eastern Pacific must rise across the reference surface
north of kO°N.
In the meridional section, there is flow eastward above 1000 m,
and flow to the west below that depth.
An additional flow of
63
lOxlO m /sec to the west is required to balance this section.
This
flow occurs as a boundary current along the Aleutians immediately to
the north of this section.
Observation of water properties indicate
that this flow is confined to the region above 1000 m.
Thus, most
of the excess northward transport at depth rises in the eastern North
L8
Pacific, enters the Gulf of Alaska gyro, and is finally transported
soothagain in the eastern North Pacific.
eransfer a: ds
at secn C
The greater southward
in the western Pacific than the zonal transport
Lg1r
rdoa°s soe sikg of water
2d
n the
western NortC Paciflc.
The general schema of the dccc water circulation agrees with
that proposed by Stornmai, Figure 6, although there is no evidence
for the intense western current, nor for the general upward transport across the 2000
surface,
in the region considered, the
upward transport appears considerably more localized.
The Surface Circulation
As has been mentioned, the surface circulation is relatively
insensitivu to shifts in the reference level.
The most apparent
results of establishing a non-constant reference surface appear in
the deep current, which, being a counter current, has the general
effect of reducing the overall transport values.
The exchange of
water between the two systems, however, is reflected in the surface
circulation and distribution of properties.
Temperature and salinity sections along 175°W and 165°E are
shown in Figures 21 to 2L..
The ridging of the isohalines south of
the Aleutian Chain (approximately latitude 50°N) is one of the dominant features of this area, and separates the westward flowing
Coastal Water (Alaska Stream) from the eastward flowing Oyashio
Water.
The location of this ridge, and the temperature and salinity
values are consistent with this analysis of upward transport in this
Li
L9
------:
/1
\
\
!
/
\
/
\\
\,
N
\
\
\
-.-
\
N
80 C
\
\
\
\
\
\
I)
\
\
5O0
35°1
titude
FIGURE 21.
Temperaturc
distribution along l75W longitude
-
---
-----
ii
)
\
oo
/
2
\2
-
/
017 C)
cJ
009
oo
1
000T
c7
r
j
Ju-
;i pU
() uoTnqT.sTp uot
0ç,'
pa-ruot
51
) );
(
;\
\\\
N
n
\
\
N
100
50°N
L5°fl
40°F
35°F
Latitude
FIGURE 23.
Temperature (°C) disLribution along 165°F longitude
52
200
600
800
1000
SOON
L5°5T
Latitude
LIGURE 2'-.
Salinity %) distribution along 165°E longitude
35°N
53
region.
A second feature of the surface property distribution,which is
rclted to the wind-induced transnorn, is the salinity front in the
surface layer identified by the
t vertical 3L% isohaine
above the salinity minimum occurring near latitude
l°N.
This lens
of high salinity water caused by an excess of evaporation over
precipitation is characteristic of Pacific Central (Sub-Tropic)
Water.
The westward transport at about 35°N does not always reach
the surface, or rise to near the surface.
The effect of the counter
flow is to maintain the distinction between the colder Oyashio water
to the north and the warmer Kuroshio water to the south.
The previous studies of the wind-driven circulation, which have.
included the Pacific, have all arrived at values of the total
transport in the Kuroshio-West Wind Drift system of about one-half
of the best observational estimates (19, p. 158-167).
Part of this
discrepancy has been attributed to use of lOW values for wind
stress, but the presence of a counter circulation in the deep water
fits the observations, and provides estimates of uowelling in the
North Pacific which accord with the observed distribution of water
properties in a manner which simply adjusting the wind stress cannot
do.
Nuromov (20, p. 24-32) has proposed a scheme of clockwise
circulation to the bottom.
This increases the difficulties with the
transport problem, for the observed transports then become 3 to 5
times the magnitude of the transport computed from wind stress.
54
Summary
Geostrophic velocities and transports have been calculated for the
summer of 1958 for the North Pacific from the surface to 5000 m.
The
distribution of properties from the surface to 1000 m was taken from
observations during the summer of 1958.
below 1000 m
The distribution of properties
was taken as the average of all available data.
Additional transport values for the North Pacific were calculated
from wind stress data averaged for July and August, 1958.
On the assumption that the circulation and transport in the
interior of the North Pacific is primarily a wind-driven system, it is
possible to choose reference depths for the geostrophic transport to
bring them into agreement with the wind transport.
To obtain reasonable
and consistent values it was necessary to average over sections from
5° to 15° wide.
Reference levels for zonal and meridional transport
are at different depths.
The surface circulation is clockwise.
There is a counter
circulation at depth, with exchange between the two layers at high
latitudes.
The computed flow patterns are consistent with the
observed distribution of properties.
55
BIBLIOGRAPHY
1.
Bennett, E.
B.
Some oceanic features of the northeast Pacific
Journal of the Fisheries Research
Ocean during August 1935.
Board of Canada 16:5655[3.
2.
Hroic, J. W. ard
ocean waters.
3.
............... .
Nature 181:107-108.
Age determinations of southern
1958.
Burkov, V. A. and M. N. Koshlyakov. 0 dinamicheskom balanse v
pole glubinnykh techeny tichogo okeana. Dokiady Akademii Nauk
SSSR 127:70-73.
14
T.
ls-99.
Charney, J. G.
1959.
The generation of ocean currents by wind. Journal
of Marine Research lLI:/477/498.
1955.
Defant, Albert.
5.
Die absolute Topographic des physikalischen
Meeresniveaus und der Druckflachen, sowie die Rasserbewegungen fin
Atlantischen Ozean. Deutsche Atlantischa Espedition Meteor,
Wissenscbaftlicbe Ergebnisse, Bd. VI,2, Tail 5:191-250. 1941.
6.
Defeat, Albert. Physical oceanography.
2 vols.
7.
Dietrich, Gunter.
8.
Dodimead, A. J. and F. Favorite. Oceanographic Atlas of the
Pacific Subarctic Region. Nanaimo, B. C., Fisheries Research
Board of Canada, Pacific Oceanographic Group, 1961. 146p.
9.
Doe, L. A. E. Offshore waters of the Canadian Pacific coast.
Journal of the Fisheries Research Board of Canada 12:1-314. 1955.
10.
Favorite, Felix and Glenn Pedersen. North Pacific and Bering Sea
oceanography, 1958. Washington, TJ S. Government Printing Office,
1959. 23Op. (U. S. Fish and Wildlife Service. Special Scientific
Report-Fisheries no. 312)
Oxford, Pergataon, 1961.
Die dynamische Bezugsflache, em
Gegenwartsproblera der dynataischen Ozeanographie. Annalen der
Hydrographie und Maritimen Meteorologie 65:506-519. 1937.
II. Fofonoff, N. P. Dynamics of ocean currents. Nanaimo, B. C.,
Fisheries Research Board of Canada, Pacific Oceanographic Group,
1961.
129p.
12.
Fofonoff, N. P. Transport computations for the North Pacific
Ocean, 1958. Nanaimo, B. C., Fisheries Research Board of Canada,
Pacific Oceanographic Group, 1960. 87p.
13.
1-lassan, E. N.
On the wind driven ocean circulation. Deep-Sea
Research 5:36-43.
1958.
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14.
Hidaka, Noji. A theoretical study on the general circulation of
he Pacific Ocean. Pacific Science 9:183-220. 1955.
15.
Nirano, Toshiyukf. On the circularion of the subarctic water.
Bu11tn of Tokci Regic:uhl Fieharies Research Laboratory
29:11-39.
1.
16.
Ihiye, T.
17.
Montgomery, R. B. Bin Versuch, den vertikalen und seitlichen
Austausch in der Tiefe der Springschicht its bquatorialen
Atlantischen Ozean zu bestimmen.
Annalen der Hydrographie und
Maritimen Meteorologic 67:2k2-250. 1939.
18.
Morgan, G. W.
On the wind-driven oceanic circulation.
8:301-320.
1956.
19.
Murk, W. H. and G. F. Carrier. The wind-driven circulation in
ocean basius of various shapes.
Tellus 2:138-167.
1950.
20.
Muromov, A. N. Scheme of the general circulation in the Pacific
Ocean. AkadamilaNauk SSSR, Izvestiia, Seriia Geofizicheskaia,
6:2L_32.
1938.
21.
Neumann, Gerhard. On the dynamics of wind-driven ocean currents.
New York University, College of Engineering, Meteorological
Papers 2:1-33, August, 1955.
22.
Neumann, Gerhard.
On the effect of bottom topography on ocean
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1960.
23.
Ostapoff, Feodor. On the depth of the layer of no motion in the
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In: Contributions to the study of the
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On the deep water in the watarn North Pacific.
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The
Te11us
Pickard, G. L. and Keith Rodgers.
Current measurements in Knight
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of Canada 16:635-678.
1959.
25.
Proudman, J.
409p.
26.
Rattray, Maurice, Cuthbert M. Love and Diane E. Heggarty.
Distribution of physical properties below the level of seasonal
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1962.
Dynamical oceanography.
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27,
Reid, Joseph L.
On the geostrophic flow at the surface of the
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1961.
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Robinson, A. aod r. S-::nmel. Th.e oceanic thermocline and the
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rculaton
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Oceanographic conditions in the Northwestern
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Equations of a field of total flow induced by the
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The circulation of the abyss.
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Stommel, Henry. The Gulf Stream.
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On the abyssal circulation of the world ocean-TI.
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An estoarine analogy in the
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59
APPENDIX
Sources of Surface Data
Vessel
11.M.C.S.Oshaaa
Station_N
DatotCrisc
l58
Fisheries Research Board of Canada, FOG.
1-111
July 22-Aug. 16
C.N.A.V. Whitethroat Fisheries Research Board of Canada. BOG.
1- 97
June 27-Au. 14
KeLj7estII
Fisheries Research Board of Canada, BOG.
May
16-June 14
Fort Ross
Fisheries Research Board of Canada, BOG.
May
10-June 25
N.y. Attu
Biological lab., Bur. Comm. Fish,Seattle
1- 78
May
7-Aug. 31
M.V.Pioneer
Biological Lab.
1-105
May
7-Aug. 31
N.V. Brown Bear
Dept. of Oceanography, Univ. of Wash.
1- 41
June 30-Aug. 20
JhihM. Smith
Bur. Comm.
Fish,Seattle
Biological Lab., Bur. Comm. Fish.,
Honolulu, Hawaii.
14-1Ol(not July 5-Sept.
consecutive)
R.V.LofuMaru
Japan Meteorological Agency, Tokyo
1005 -1009
1039-1049
1055-1061
HaV. Spyo Maru
Tokai Regional Fisheries Research Lab
T.S. Ilokusei Maru
Faculty of Fisheries, }-Iokkaido Univ.
1- 29
June 10-June 25
Faculty of Fisheries, Hokkaido Univ.
1- 22
June
1- 17
22- 43
July
28-pt.
3
11
7-June 27
61
Sources of Deep Station Data
Number
Source of Dota
Norpac data, O.O.P.S. 1955:
Stut5.ons
}lorizon
Black Douglas
Oshoro Maru
Yushio Maru
Ryofu Maru
Tenyo Maru
Brown Bear
F.R.B. Canada, Phys.-Chem. Data
Record, N. Pac. Survey, Ms.
Report Series:
No. 4
No. 16
No. 28
No.
49
No. 59
No. 98
No. 54
No. 54
No. 63
No. 82
No. 82
No. 106
University of Washington:
Tech. Rapt. No. 49
Spec. Reat. No. 29
S2eo. Rapt. No. 30
Japan Nat. Comm. F., IGY
1GY 124.1 B-4
ICY 124.1 B-S
Nat. Oceanographic Data Canter:
ICY 124.5 A-1
ICY 124.3 A-i
ICY 124.3 A-4
ICY 137.1 B-2 Cruise 25
IGY 137.1 B-3 Cruise 26
IGY 137.1 B-4 Cruise 27
ICY 137.1 B-S Cruise 29
S.I.O. Mukluk
S.I.O. Chinook
S.1.0. Transpac
Oshawa
Oshawa
Wtitethroat
Whitethroat
St. Catharine
St. Catharine
Oshawa
Whitethroa-t
Beacon Hill
Whitethroat
Oshawa
St. Catharine
Brown
Brown
Brown
Ryofu
Ryofu
Ryofu
Bear
Bear
Bear
Maru
Maru
Maru
Soyo Maru
Takuyo
Takuyo
Vitiaz
Vitiaz
\Titiaz
Vitiaz
Horizon
Baird
Horizon
14
6
1
3
3
15
34
41
32
3
4
4
27
57
41
23
30
7
43
8
13
10
8
1
9
6
3
I
5
4
3
64
12
9
35
Date
Aug 1955
Aug 1955
Jul 1955
Aug-Sep 1955
Aug-Sep 1955
Jul-Sep 1955
Aug-Sep 1955
Jul-Aug 1957
Mar-Apr 1958
Jun-Aug 1958
Apr-Sep 1958
Mar-Nay 1959
Mar-Dec 1960
Aug 1959
Aug 1959
Jan-Feb 1960
Jul-Aug 1960
Jul 1960
Jan-Aug 1961
Aug 5LJan 55
Aug-Sep 1957
Jul-Aug 1958
Jul-Sep 1958
May 1959
Nov 1959
Aug 1958
Oct 1957
Mar 1959
Jul 1957
Nov 1957
Mar-Apr 1958
Oct-Dec 1958
Jul-Aug 1957
Jul-Aug 1956
Aug-Oct 1953
62
LIST OF SYMBOLS
f
g
p
U
V
w
x
y
z
ZE
AH
B
D
AD
p
U
UB
Ug
Us
Uw
V
VB
VE
Vg
VS
vw.....
coriolis parameter = 2csin4)
acceleration of gravity
pressure
x-component of velocity
y-component of velocity
z-component of velocity
horizontal coordinate (+ to east)
horizontal coordinate ( to north)
vertical coordinate (+ 'upwards)
depth to bottom
horizontal eddy viscosity
vertical eddy viscosity
bottom
dynamic height
dynamic height anomaly
potential energy function
pressure at bottom
zonal transport
barotropic zonal transport
Ekman zonal transport
geostrophic zonal transport
geostrophic component of wind-driven zonal transport
wind-driven zonal transport
meridional transport
barotropic meridional transport
Ekman meridional transport
geostrophic meridional transport
geostrophic component of wind-driven meridional
transport
wind-driven meridional transport
specific volume
latitudinal gradient of the coriolis parameter
surf ace elevation
latitude
gravitational potential
density
stress
angular velocity of earth's rotation
63
MAT1iEATICAL DEIUVATIONS
The Geostroohic Ecuation
The derivation sivan hera is devecaed i. s manner similar to that
used by Fofonoff (11, p. 22-2).
We use a potential function
defined so that its difference at
two levels is equal to the work per unit mass recuired to move a body
from one level to the other.
The coordinate z has been chosen parallel
to the direction of action of gravitational acceleration so that
is a function of z only.
Surfaces of constant z correspond to surfaces
of constant gravitational acceleration potential (geopotential).
The
geopotential is related to height z and gravitational attraction g by
the equation
(la)
Thus, the geopotential at any level z is
(2a)
where
(z
is the geopotential at the origin of the coordinate system
0).
The geopotential can
sea water and pressure by
expressed in terms of specific volume of
ns of the hydrostatic equation
J
(3a)
61
integrating (3a) we obtain
Ap
(-)
(-)
=
(
(#a)
The geopotential relativu to the
urace of the ocn (P
0) is
(5a)
Now the differential equations defining
eostrophic flow have been
given (p 23) as:
a)
Where
and
are taken on surfaces of constant
ie may express.
the pressure gradient on a geopotential surface as a geopotential
gradient on an isobaric surface by the relations
(a
-
But
xJ
/()
/
from (3a)
Thus
(7a)
Thus equations (7a) become
I,
(8a)
I
34t
/
'P
65
Since the derivatives are taken along isobaric surfaces, an
arbitrary function of pressure may be subtracted from
without
Thus
affecting the values of the darivatives.
r
j
where
(9a)
j
is specific volume of sea water at 0°C
nd 350/00 salinity,
is the anomaly of specific volume.
but a function of pressure, and
Re can express the geostrophic equations as
-
r
i--c)-
(iDa)
3Lwhere the anomaly o
geopotential, or "dynamic height",
D is defined
by
C)
At the ocean surface, P = 0 and thus
(ha)
D(P) = 0, and the geostro-
phic equations reduce to
r
--
I
0
(12a)
4 A4
-
so that equations (hOe) can be written
(l3a)
p
66
or the velocity at any surface relative to the velocity,
-() , at a
reference surface is given by:
r
(r)
-
-
_-
(lLa)
r
,(v1
L.
which has been used in the text as equation 7.
Total Transport Equations
The simplified hydrodynamical equations, page 25, are:
-
- 4-
I
0
I
-:
-fr 4
__z
(15a)
integrating equations (l5a) vertically from the bottom to the surface
of the ocean, and substituting from the following definitions:
f
rd
I.
67
We obtain:
,
F
(17a)
L
J
The boundary conditions at the surface and at the bottom of the
ocean are:
L3&
_.-.
/
)
,,
v
(18a)
'
Where
are the components of the wind stress at the surface,
y and
and
are the bottom stress, equal to zero since the velocity
gradients approach zero near the bottom of the oceans.
Further, we may expand the expression for the integral of the
pressure gradient:
J(19 a)
We adopt the notation for the integral of p:
(20a)
lJsing the relatioas of (l8a), (19a) and (20a), equations (l7a) may
be written:
-v
-
(_
;
c
(21a)
)
Now the geostrophic flow along the bottom will be a balance of
conchs forces and the bottom pressure-gradient forces.
Writing the
y-equat ion only:
-
3
(/; ')
L
(22a)
And, using (22a)
we define
fre barotropic transport:
/;
()
(23a)
Thus;
-
()
(2a)
Similarly, the baroclinie oornponents of velocity give rise to
baroclinic transports:
ri,
JL4S
-
(25a)
I.
Introducing the Ekman transport components,
UE
and
VE
defined by:
IJE
=
(26 a)
=
Equations (21a) may now be written, substituting from (2L1a), (25a)
and (26a):
U
=
V
= VS+VB+VE
(27 a)
Equations (27a) have been used in the text as equations (23) and
(214), page 28.