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Models of the diffusive–advective balance at the subtropical convergence
)eep-SeaResearch,1976,Vol.23, pp. 1153to 1164. PergamonPress. Printedin GreatBritain
Models of the diffusive-advective balance at the Subtropical Convergence R. A. HEATH* (Received 14 November 1975; in revisedfi~rm 7 May 1976; accepted 13 May 1976) Abstract Horizontal and vertical diffusion coefficients are calculated by fitting different types of diffusive advective models to the scales of a specified anomaly in the salinity field near the Subtropical Convergence. Comparison of the calculated coefficients with those in the literature reveal the balance in the mixed layer near the convergence is between horizontal diffusion and northward advection. Below the mixed layer at the convergence the balance is between southwards and upward advection and mainly horizontal diffusion. A tongue of saline water extends south from the convergence with its core at a depth of about 100 m. The balance in this tongue is consistent with a uniform slow northwards flow with parabolic shear and horizontal and vertical diffusion.
INTRODUCTION
THE BOUNDARYat about 45°S between the warm saline subtropical water in the north and the cooler less saline subantarctic surface water has been called the Subtropical Convergence. DEACON (1937) showed that at the surface the position of this convergence is marked by a sharp temperature and salinity change (usually of the order of 4 to 5°C, 1~,,,,in short steps over a distance of about 200 km) (cf. DEACON, 1945). The sharp change in properties across the convergence has been considered to be maintained by convergent motion between meridional components of surface currents (see e.g. GARNER, 1959; DEACON, 1945). Deacon also found that from the Subtropical Convergence a high-salinity subsurface tongue can extend nearly as far south as the Antarctic Convergence (a distance of about 1400 km). This subsurface layer is found at depths between 100 and 300 m in the Atlantic Ocean and western side of the Indian Ocean and at somewhat greater depths in the Pacific Ocean. Most schematic meridional sections of the Antarctic Convergence-Subtropical Convergence regions show a southwards movement of this salinity maximum with a northwards movement of water both above and below (e.g. SVERDRUP, JOHNSON a n d FLEMING, 1942; GORDON, 1971). This mer-
idional circulation pattern is apparently inferred from the presence of the tongue rather than being based on current measurements. In this paper several simple diffusive-advective models are fitted to the salinity field near the Subtropical Convergence. Comparison of the diffusion coefficients derived from the models with those in the literature then allows at least the qualitative validity of the models to be tested and hence gives some understanding of the main advective-diffusive balances in the region. The data used are four near-synoptic meridional sections, one west of New Zealand and three east of New Zealand (Fig. 1, Table 1). These probably provide the only sets of closely spaced near-synoptic data across the Subtropical Convergence. THE SALINITY ANOMALY
The sub-surface salinity tongue extending southwards from the Subtropical Convergence (Fig. 2) can be represented by an anomaly in the salinity field. This anomaly S' is related to the observed temperature (T) and salinity (S) by the T/S relationship S = m T + S'+ a; m and a are con*New Zealand Oceanographic Institute, Department of Scientific and Industrial Research. P.O. Box 12-346, Wellington North, New Zealand.
1153
1154
R.A. HEATH
165°E
l
c--'t
~'~
170 °
175 °
I
I
175°w.,
180 °
I
I1
#
9
I)612 10951
F952
~794
0608
~/////~
45'
L~IH790
D601 6 LINE 2
F955
E3
Y
F957
<
N
.p.)o°°
,~
<~
Fig. 1. Station positions of the data used in the cross-sections and the position of the Subtropical Convergence (hatched).
stants. Further, it obeys the same diffusion equation as the observed salinity S, assuming that the vertical and horizontal Austauch coefficients, K~., Kn, respectively, are constant and the same for both heat and salt (see NEEDLER and HEATH, 1975), i.e. OZS' v'VS' = K v ~ + K , V o2S , where v is the velocity, Z the vertical coordinate positive downwards and V2 the horizontal Laplacian. Specification of this anomaly allows the tongue to be studied separately without having to consider the overall dynamics associated with a
Table 1. Source of station data used. Station
Month/year occupied
Source of data
Di 921 D i 824 D 601-D 612 G 790 -G 798 F 950-F 957
June 1932 April 1967 May 1970 January 1969
GARNER (1962) HEATH (1968) HEATH (1973) RIDGWAY(1975)
T/S relationship changing with position. The linear T/S relationship S O = roT+a, from which the anomaly is defined is that of the Subantarctic Water south of the Subtropical Convergence (Fig. 3).
Models of the diffusive-advectivebalanceat the SubtropicalConvergence
D615 •
[:)612
~.:a'.._
{///
D609
////
/
D~e
~
1155
[7o01
tI
-4"---"-" 400
I.u
/
o 1400
!i
1600
.1/"
•6 ~
Chatham Rise
220(3
240(3
0
100
200
300
400
500
km
Fig. 2.
Meridional salinity (%o) cross-section across the Subtropical Convergence at longitude 177°40'E. Isopycnals o f a t are also
shown. THE M E R I D I O N A L S A L I N I T Y D I S T R I B U T I O N NEAR THE
Subtropical Convergence indicate three distinct patterns of the isohalines:
SUBTROPICAL CONVERGENCE
Plots of the salinity anomaly across the Subtropical Convergence along 177°40'E, 179°00'E and 174°00'W are shown in Figs. 4, 5 and 6, respectively. The first two are over the zonally oriented Chatham Rise east of New Zealand--in this region the convergence has very little variation in position, being confined to the Chatham Rise, which directs the flow zonally. The other sections (Fig. 6 and at 163°50'E) are away from any immediate topographic influence, although that at 163°50'E is probably influenced by the New Zealand landmass while that at 174°00'W is immediately east of the Chatham Rise (Fig. 1). Distributions of the salinity anomaly across the
(a) a region south of the Subtropical Convergence where there is a sub-surface tongue of saline water. The distribution in this tongue is not monotonic (Figs. 5 and 6) for there are areas of significantly higher salinity imbedded in it. (b) North of the convergence a mixed layer (upper 50 m) is generally developed. The salinity in this layer decreases rapidly towards the south near the Subtropical Convergence. (c) A region below the mixed layer in mainly Subtropical Waters where the salinity decreases both towards the south and vertically downwards.
SALINITYo~
34.2 .3 .,: .5..;
.,7 ,y .~a~o.]
Relevant vertical and horizontal scales in each region for the meridional sections have been obtained by least-squares fits (Table 2). We will first test the consistency of different diffusive-advective balances with the scales of the saline tongue south of the Subtropical Convergence. The compatibility of the flow field in these models with that in the major diffusive advective balance at the convergence are then examined. The models are described by
.~ .3..4. -5 .9
tg
e,.-,
18!
So=rnT+a
17
/'/ i~/,/' D612
15
P 14 l
~
\
1|
I ~,
5 4 3 2 t
J *,/2"
'l
10
,,'/
,.,.'" ,/
8S' 8S' 82S ' 82S ' W g~ + v-= K,. + Kn
"d
f(
Fig. 3. Temperature salinity diagrams for stations on the section along longitude 177°40'E.
°
(1)
-2
-4
S~ •
~
I
. . . . . /
43 °
0612
,
';/~ f 1"1~ 1
where y is the horizontal coordinate positive to the south (i.e. essentially perpendicular to the Subtropical Convergence) with associated velocity component v; W is the vertical velocity component. Zonal changes in salinity near the Subtropical Convergence are small (see e.g. RIDGWAY, 1975) and therefore the zonal advection term u 8 S / ~ x can be ignored. 44 °
~
DeW
,' : •
o •
46 °
46 °
De06
DeOI
',.' •
l
•
•
• •
/ i
/
•
•
/
" -
S%°'75
2f
"~',~.
--
<
Surfaoe Salin~ Anorr~y
"-. I00
200
300
y(km)
Fig. 4. Meridional salinityanomaly (Too)cross-sectionacross the Subtropical Convergence at longitude 177°40PEI Plots of salinityanomaly with depth at Sta. D612 and horizontal distance are also shown.
1156
S%o 0-2 0-4 0-6
'~
42°S G?g8
43 ° G79'7 G796 GTg5
44 °G794
45° G792
G793
/
/
300
,"
400
I
,
•
:/.
•
.
.."
"
!
50~
46° G791
•
0 " 2 . ~
60(3
I !
•
J
80~
R~e
100C
'11~%.%%SalinityMaximum
S%,o0~4~I
1200
s% e4
1500
~ |
Fig. 5.
|
I
;,
.
-
20o ~w) 30Okm Meridional salinity anomaly (~oo) cross-section across the Subtropical Convergence at longitude 179~00'E. Plots of salinity anomaly with depth at Sta. G798 and horizontal distance are also shown. 43°S
s%o 0
0
"2
,
-4
•
44 °
45 °
F~I F~2
'6
•
46 °
47 °
°etF~=
48 °
R~
49 °
50 °
F~7
•
loo 2oo
/
3oo
//
4oO
/
soo ~6oo 700
/
I
/
/ I I I
0, 100o,
12o(3 •
°'6F e ' ~ , , , ° S°/oo
O'4]/
0"2 z • 0
00
Fig. 6.
SO
IO0
..Salty
%ql,~.~ Mamimum
' * / I. 50 100 150 ~ 0 k m
150
200
~0
S00
~0
400 , ~ k m
Meridional salinity anomaly (%0) cross-section across the Subtropical Convergence at longitude 174°W. Plots of salinity anomaly with depth at Sta. F951 and horizontal distance are also shown. 1157
1158
R.A. HEATH
Table 2. Observed scales and salinity anomalies and quantities derived from the diffusive-advective models Observed scales and salinity anomalies Longitude of meridional section
Vertical scale h (m) S0 exp( - Z )
Line 1 163°50'E Line 2 177'~00'E Line 3 179°00'E
Line 4 174°00'W
Region a Region b Region c Region a Region b Region c Region a Region b Region c *Region a Region b Region c
Horizontal scale L (km)
S0 e x p ( - ~ )
S0 (%o)
So (?~o)
S0 exp( - y )
400
0.18 0.50
0.19 0.38 0.38
3000 840 840
0.2
0.25
600 220
1.3
1.2
230 75 75
0.49
0.48 0.6 0.6
95 95 95
0.54 0.7 0.7
350 310 310
1,2
226 150 510
0.5 500
460
0.42 0.6
* Not well defined. Note: Region a = south of the Subtropical Convergence in the saline sub-surface tongue. Region b = in the mixed layer where the salinity decreases rapidly towards the south. Region c = below the mixed layer in mainly Subtropical Water where the salinity decreases both towards the south and vertically.
THE SUBSURFACE TONGUE OF SALINE WATER SOUTH OF THE SUBTROPICAL CONVERGENCE
It is tempting to assume that this tongue is simply associated with a vertical shear in the horizontal velocity profile. The two main components of meridional flow in this area are the geostrophic flow and Ekman drift. The relative meridional geostrophic velocity along latitude 43°S in the Pacific Ocean has been calculated using the Eltanin Cruise 28 (SCORPIO Expedition, 1969) data (Fig. 7). Also, the meridional geostrophic flow relative to 400 dbar near 43°S 149°W and 28°S 140°W has been calculated from the Eltanin stations and the meridional Ekman velocity (using a large value for the eddy viscosity
coefficient of 400 g cm- 1 s- 1) calculated from wind stress data (HIDAKA, 1958) for this locality (Fig. 8). The meridional velocities along 43°S are generally between 0 and 1 cm s-~ to the north. There is little shear in the meridional geostrophic flow at 43°S, but substantial shear both in the meridional geostrophic flow at 28°S and in the upper 100 m in the directly wind-induced flow. The depth of the turning point in the directly windinduced flow is, however, considerably shallower than the depth of the maximum salinity. Direct current measurements made by the author with two parachute drogues, one at 25 m the other at 150 m, near 43°56'S, 178°E, indicated a slow northwards meridional component with very little relative shear over a tidal cycle although there are periods of large shear within the cycle.
Models of the ditfusive-advective balance at the Subtropical Convergence
Table 2.
Continued Models of the Subtropical Convergence
Models of the salinity tongue
K,,
Horizontal scale (km) for pure diffusion, Observed values in brackets
1159
Direction of w
Direction *Iv
- - for no v horizontal diffusion
w
Horizontal diffusive and advection Kn
v
Vertical diffusive and horizontal advection
ge
Ivl
Pvl 381
(3000)
9 South
190
(230)
140
34
(95)
190
4.6 × 107 Not defined
South
Upwards
3.4 x 10 3
1 x 105
87
North
Downwards
1.2 x 10 -3
8.8 x 106
406
37
(350)
110? Not well defined
170
160
150
140
130
LONGITUDE 120
110
100
90
80
70°W
~3,5
~034 Surface Salinity along 28°S (+) and 43°S (o)
Key
qorth
X
Vo- 1500 Vo-4000 + Vo-3500 * V250-1500 •
~,,s
~ou~
*
Meridional Velocity along 43°S
Fig. 7. Meridional geostrophic flow at the surface relative to different reference levels for the leg of EItanin Cruise 28 along 43°S (SCORPIO Expedition 1969) across the Pacific Ocean. The surface salinity (%0)along latitudes 28 and 43°S are also shown.
1160
,South - 4-1'2 '
~
R.A. HEATH
-1
,
-8
•
-'6
i
4
-'2
w
i
'
Cms 0
2 !
'4
6 ;. -
-2oo
"8 -
-
'2 .
14 .
1-6 .
North 1"8 2 • ' ,
of the form s' =
)
.4oo
[I
•8oo
I
-8oo
where now the axes are such that Z = 0 along the salinity maximum which approximately coincides with an isopycnal.
I
-1000
/
I
A complete solution for S is given by the Fourier Series
•1 2 0 0 I
I
I
S = ~ DmcosmZe -k(m);,
I •2t~ °--- 1 5 ' S
rn=O
where m is an integer and k is related to m by
I
k = K~, +_ ~300
S=
o
Fig. 8. Meridional geostrophic velocities with depth relative to 3500 m between Stas. 40 (127°36.0'W)and 50 (150°35.0'W) along 43°S, and Stas. 122 (130°02.8'W) and 133 (150°51.0'W) along 28°S from EItanin Cruise 28 (SCORPIO Expedition 1969). The meridionai Ekman velocity with depth for wind stress of 0.41 dynes cm ~ at 83°T taken from HIDAKA (1958) for the region 152.5 to 137.5°W, 42.6°S is also shown.
These scant observations indicate that in the region of the saline tongue the mean meridionai flow is very weak and northwards with only slight shear in the geostrophic flow. However, shear will be frequently imposed by the directly windinduced flow. We will therefore first consider simple models with uniform flow with depth and then examine the effects of current shear. Several of the salinity profiles across the Subtropical Convergence show isolated patches of high-salinity water in this subsurface tongue (Figs. 5 and 6), which indicate horizontal transfer in this tongue is probably highly time dependent. In the models we have smoothed these patches and are looking at this smoothed salinity field.
No velocity shear
O2S' ~2S' = K . ~u y - + K~, 8Z 2'
Dm cos mZ e-k(m)~'din.
This solution can be fitted to an arbitrary salinity distribution at y = 0 which is taken as S = So exp ( - rZZ 2). Then
Dm = ~2 f f
Soexp(-r2Z2)c°smZdZ'
(e.g.p. 454, MORSEand FESHBACH, 1953), which on using the integral
fo°
e x p ( - a 2 x 2)cos bxdx = 2 a e X p
(2)
- ~
gives
Om:So J( )exp( ) and /'/1
S=SoJo
m 2'
L ~ / ~ r z ) e x p ( - ~ r 2 ) c°smZ
x exp{-yL[-1
For the case of constant flow we look for a solution to
8S'
K,, "
In integral representation this gives
kSO0 Depth(m)
v~-
Kf, + 4m2 K~J]/
+ ~ / ( 1 + 4m2KuK~'~lv2 JJ
,
Models of the diffusive-advectivebalanceat the SubtropicalConvergence For v positive the positive sign in front of the square root is taken and for v negative the negative sign. These choices allow the salinity to decrease towards the south. We will now consider different balances of equation (2).
1161
S0 ~4\
v
× exp
4(~+
(6)
Case I. No advection (v = O) Equation (3) reduces to ~.2) ~
din.
cos mZ exp
\/~]3 (4)
and the meridional flow is southwards. Again we wish to compare the horizontal scale of this solution with that observed in the tongue. On the 1' axis (Z = 0) we have S
1
We wish to compare the horizontal scale of this solution with that observed in the tongue. On the y axis (Z = 0), equation (4) gives Using the horizontal scales L = y, where (S/So) = e- 1 gives values of K~/v ranging from 9 to 37 for the first three lines (Table 2). Unless the meridional velocity is remarkably small (~0.05 cm s- 1) the sizes of these vertical diffusion coefficients are very which has a solution (ERD•LYI, MAGNUS, much larger than the typical upper values of OBERHETLINGESand TRICOMI, 1954, p. 146) 1 cm 2 s- 1. This would indicate that the balance in this tongue is not simply between vertical diffusion S= So exp(rZy z K~) and horizontal advection. Further, if horizontal diffusion is included and the flow is still towards ×[1-2g-a/2forY~(~)exp(-t2)]dt. (5) the south the vertical diffusion coefficient would need to be still larger. The horizontal scales L[S=Soexp(-y/L)] evaluated from equation (5) for three of the lines Case 3. Vertical and horizontal diffusion, horizonusing a value of (Ku/K~) = 106 are given in Table tal northwards advection 2. On the sections over the Chatham Rise these Equation (3) was integrated numerically, using horizontal scales are close to those observed. For the adaptive Simpson method using interval bisecthe section away from the constraining influences tion (e.g. MCKEEMAN, 1962). The values of Kdv, of the Chatham Rise (lines 1 to 4) the horizontal Ku/v and r were varied and S/So computed at scale is substantially less than that observed, different positions (Z, y). The horizontal exponenindicating that here probably horizontal advectial scale e x p [ - (x/L)] calculated from these disttion has a strong influence. ributions for various ranges of parameters is given in Table 3. For the range of vertical scales of Case 2. No horizontal diffusion (K n = O) interest here, exceedingly large values of K,,/v are Equation (3) reduces to needed before vertical diffusion plays a role in determining the horizontal scale. Also, the vertical S = S o /' 1 cosmZ scale is constant along the tongue. Alternatively, the vertical scales need to be very small before vertical diffusion, with acceptable values of K jr, x exp - m 2 + 4rfi dm plays a role in determining the horizontal scale.
×foeXpl-m~/(~--~)Y-4F]din'
1162
R.A. HEATH
Table 3, Values of the horizontal exponential scale 7 calculated by numerical integration of S
,~,
1
~/( 1 + 4m2KnK~)]/ 2Kndm : )31 K,.
×exp(-YV][-l±
\
K,,)I_
K o K~ i for different values o f - - , - - and r = - - . v v H
H
K~,
Kn
?
(m)
-v (cm)
-v (cm)
(kin)
75-500 75-500 75-500 75-500 75-500
0.1 0.1 0.1 0.1 0.1
---, 3.2 ~ 3.2 ~ 3.2 ~ 3.2 ~ 3.2
2× 4× 8× 16 × 32 ×
106 106 106 106 106
20 40 80 160 320
The model gives acceptable values of Kn/v between l0 T and 3 x 108 cm, the values being greatest on the lines away from the restraining influence of the Chatham Rise. Velocity shear To examine the effect of velocity shear we can express the meridional velocity as a constant Vo and a component varying with depth v(Z), i.e. ~S'
~2S'
~2S'
{Vo + v ( Z ) ] - ~ - = K n ~3y - 2 + K~ OZ 2 " cy A solution of this equation of the form S = So e -ty e -ky(z~ exists if K n 12
I f " t Z ) - ,--~-[Vo + V(Z)]
Kv k
kf'(Z) 2 = O,
where Vo is chosen such that where (O2S/OZ2) = v(Z) = 0, v = v0. The horizontal scale then is determined by Kn/v in a similar manner to case 3 above. However, the vertical salinity distribution is determined by the current shear and vertical diffusion. For a realistic difference in wind drift of 0.01 m s- ~ over the top 100 m the vertical diffusion coefficients for the observed vertical scales of the first three lines are 0.07, 1.1, 1.4cmZs -1, respectively. Alternatively, the geostrophically observed difference in speed in the upper 100 m on line 2 of 0.005ms-1 gives a vertical diffusion coefficient of 0.6 cm 2 s- a on that line. The balance in the sub-surface saline tongue appears to exist between slow northward advection and both horizontal and vertical diffusion with the vertical scale being determined by slight shear in the horizontal flow and vertical diffusion. We wish then to consider the compatibility of this proposed meridional circulation with the major balance at the Subtropical Convergence. D I F F U S I V E - A D V E C T I V E BALANCE AT THE SUBTROPICAL CONVERGENCE
North of the Subtropical Convergence the geostrophic meridional flow is towards the south (see e.g. Fig. 8). However, the latitude of zero zonal wind stress is about 35°S (HELLERMAN, 1967) which is generally north of the latitude of the Subtropical Convergence (DEACON, 1945, Fig. 4). Therefore the meridional component of the surface wind drift at the convergence will be towards the north. Within the mixed layer at the Subtropical Convergence the probable advective diffusive balance is between horizontal advection and diffusion described by ~S' c~2S' V~y = K H Oy2
which gives
Kn
-
[-
1
V0
and
The horizontal profile appears to be exponential in form with a simple solution S = S'o e - ylL,
kKv v(Z) = [ f " ( Z ) - k f ' ( Z ) z] - l '
where L = (g./Ivl) for v which must be towards the north. The values of Kn/Ivl for the four sections
Models of the diffusive-advective balance at the Subtropical Convergence
are given in Table 2. They range from 7.5 to 3.1 × 107 cm, being smallest where the convergence is confined to the Chatham Rise which is where the meridional flow would probably be least. Below the mixed layer at the Subtropical Convergence the isopycnals slope sharply upwards (Fig. 2), and the balance would appear to involve both horizontal and vertical advection and diffusion, described by 8S'
W~
8S'
+ v
cY
82S '
= Kn
~
(~2S'
+ K,,
~Z 2 •
Both the horizontal and vertical profiles decay approximately exponentially and a solution with constant flow is s' = So e -pr e -jz,
(7)
where -pv-jW
= Knp 2 + K~f .
In lines (1, 2 and 4) the meridional flow will be towards the south, thus the vertical flow must be upwards. However, in the region of line 3 the meridional flow was northwards (Fig. 1, HEATH, 1973). A crude estimate of the ratio of vertical to meridional flow is given by the slope of the isopycnals, assuming the flow is essentially along isopycnals and the zonal change in properties is small. This gives value of 1 to 3× 10-3cms -~ (Table 2), values which as expected are large compared with the typical downward vertical velocity of 1 to 5 × l0 -4 cm s- x below the frictional layer, which is required to balance the curl of the wind stress. Substitution of the scales in equation (7) shows that the role of vertical diffusion in this region is small compared with horizontal diffusion (Table 2).
DISCUSSION
In brief the meridional circulation at the Subtropical Convergence over the Chatham Rise appears to consist of northwards flow in the mixed layer with southwards and upwards flow below. This is consistent with the limited available current observations and simple diffusive-advective balances, horizontal advection and diffusion in the
1163
mixed layer, and mainly horizontal diffusion and horizontal and vertical advection below the mixed layers. The balance in the saline tongue extending south from the Subtropical Convergence is mainly between horizontal diffusion and northwards advection, with the vertical scale being determined by weak shear in the horizontal flow (parabolic in form in the model with the slowest flow at the axis of the tongue) and vertical diffusion. No attempt has been made to match together the three distinct distributions, for the process is obviously very complex. However, it would appear that the tongue is generated at the Subtropical Convergence by the shear in the upper few 100 m. Accepting the meridional circulation as proposed above the balances give values of Kn/v of 10 6 to 108cm, values which are in the range of those found in other studies (e.g. HAN-HSlUNG a n d VERONIS, 1970; NEEDLERand HEATH, 1975). The balances, however, do not allow the size of K d v to be established in any detail. Acknowledgements The author would like to thank Dr A. E. GILMOUR of the New Zealand Oceanographic Institute, D.S.I.R. for helpful discussion and Dr R. WOODING, Applied Mathematics Division, D.S.I.R. for help with the numerical integration computation.
REFERENCES DEACON G. E. R. (1937) Hydrology of the Southern Ocean. "'Discovery" Reports, 15, 1-124. DEACON G. E. R. (1945) Water circulation and surface boundaries in the oceans. Quarterly Journal of the Royal Meteorological Society, 71, 11-23. ERDI~LY1A., W. MAGNUS, F. OBERHETL1NGESand F. TRICOM] (1954) Table of integral transforms, McGraw-Hill, Vol. 1,391 PP. GARNER D. M. (1959) The Subtropical Convergence in New Zealand surface waters. New Zealand Journal of Geoloyy and Geophysics, 2, 315-337. GARNER D. M. (1962) Analysis of hydrological o bservations in the New Zealand region 1874-1955. Memoirs. New Zealand
Oceanographic Institute 9. (Bulletin of the New Zealand Department of Scientific and Industrial Research 144.) GORDON A. L. (1971) Oceanography of Antarctic waters. In: Antarctic oceano#raphy, I. J. L. REID, editor, Antarctic Research Series Vol. 15, pp. 169-203. HAN-HsIUNG K. and G. VERONIS(1970) Distribution of tracers in the deep oceans of the world. Deep-Sea Research, 17, 29-46. HEATH R. A. (1968) Geostrophic currents derived from oceanic
[164
R.A. HEATH
density measurements north and south of the Subtropical Convergence east of New Zealand. New Zealand Journal of Marine and Freshwater Research, 2, 659-677. HEATH R. A. (1973) Direct velocity measurements of coastal currents around the southern half of New Zealand. New
Zealand Journal ~f Marine and Freshwater Research 7, 331 367. HELLERMANS. (1967) An updated estimate of the wind stress on the world ocean. Monthly Weather Review, 95(a), 607 626. HIl~AKA R. (1958) Computation of the wind stresses over the oceans. Records of Oceanographic Works in Japan, 4, 77- 123. MCKEEMAN W. M. (1962) Algorithm 145' adaptive numerical integration by Simpson's rule. Communications. Association ./or Computing Machinery, 5, 604.
MORSE P. M. and H. FESHBACH (1953) Methods of theoretical physics, McGraw-Hill, 1978 pp. NEEDLER G. T. and R. A. HEATH (1975) Diffusion coefficients calculated from the Mediterranean salinity anomaly in the North Atlantic Ocean. Journal ~/ Physieal Oeeanoqraphy, 5, 173 182. RIDGWAYN. M. (1975) Hydrology of the Bounty Island region. Memoirs. New Zealand Oceanographic Institute, 75. SCORPIO EXPEDITION (1969) Physical and chemical data from the SCORPIO Expedition in the South Pacific Ocean, Scripps Institution of Oceanography Reference 69-15. Woods Hole Oceanographic Institution Reference 69-56. SVERDRUP H. U., M. W. JOHNSON and R. H. FLEMING (1942)
The oceans: their physics, chemistry and general biology, Prentice-Hall, 1087 pp.
Models of the diffusive-advective balance at the Subtropical Convergence R. A. HEATH* (Received 14 November 1975; in revisedfi~rm 7 May 1976; accepted 13 May 1976) Abstract Horizontal and vertical diffusion coefficients are calculated by fitting different types of diffusive advective models to the scales of a specified anomaly in the salinity field near the Subtropical Convergence. Comparison of the calculated coefficients with those in the literature reveal the balance in the mixed layer near the convergence is between horizontal diffusion and northward advection. Below the mixed layer at the convergence the balance is between southwards and upward advection and mainly horizontal diffusion. A tongue of saline water extends south from the convergence with its core at a depth of about 100 m. The balance in this tongue is consistent with a uniform slow northwards flow with parabolic shear and horizontal and vertical diffusion.
INTRODUCTION
THE BOUNDARYat about 45°S between the warm saline subtropical water in the north and the cooler less saline subantarctic surface water has been called the Subtropical Convergence. DEACON (1937) showed that at the surface the position of this convergence is marked by a sharp temperature and salinity change (usually of the order of 4 to 5°C, 1~,,,,in short steps over a distance of about 200 km) (cf. DEACON, 1945). The sharp change in properties across the convergence has been considered to be maintained by convergent motion between meridional components of surface currents (see e.g. GARNER, 1959; DEACON, 1945). Deacon also found that from the Subtropical Convergence a high-salinity subsurface tongue can extend nearly as far south as the Antarctic Convergence (a distance of about 1400 km). This subsurface layer is found at depths between 100 and 300 m in the Atlantic Ocean and western side of the Indian Ocean and at somewhat greater depths in the Pacific Ocean. Most schematic meridional sections of the Antarctic Convergence-Subtropical Convergence regions show a southwards movement of this salinity maximum with a northwards movement of water both above and below (e.g. SVERDRUP, JOHNSON a n d FLEMING, 1942; GORDON, 1971). This mer-
idional circulation pattern is apparently inferred from the presence of the tongue rather than being based on current measurements. In this paper several simple diffusive-advective models are fitted to the salinity field near the Subtropical Convergence. Comparison of the diffusion coefficients derived from the models with those in the literature then allows at least the qualitative validity of the models to be tested and hence gives some understanding of the main advective-diffusive balances in the region. The data used are four near-synoptic meridional sections, one west of New Zealand and three east of New Zealand (Fig. 1, Table 1). These probably provide the only sets of closely spaced near-synoptic data across the Subtropical Convergence. THE SALINITY ANOMALY
The sub-surface salinity tongue extending southwards from the Subtropical Convergence (Fig. 2) can be represented by an anomaly in the salinity field. This anomaly S' is related to the observed temperature (T) and salinity (S) by the T/S relationship S = m T + S'+ a; m and a are con*New Zealand Oceanographic Institute, Department of Scientific and Industrial Research. P.O. Box 12-346, Wellington North, New Zealand.
1153
1154
R.A. HEATH
165°E
l
c--'t
~'~
170 °
175 °
I
I
175°w.,
180 °
I
I1
#
9
I)612 10951
F952
~794
0608
~/////~
45'
L~IH790
D601 6 LINE 2
F955
E3
Y
F957
<
N
.p.)o°°
,~
<~
Fig. 1. Station positions of the data used in the cross-sections and the position of the Subtropical Convergence (hatched).
stants. Further, it obeys the same diffusion equation as the observed salinity S, assuming that the vertical and horizontal Austauch coefficients, K~., Kn, respectively, are constant and the same for both heat and salt (see NEEDLER and HEATH, 1975), i.e. OZS' v'VS' = K v ~ + K , V o2S , where v is the velocity, Z the vertical coordinate positive downwards and V2 the horizontal Laplacian. Specification of this anomaly allows the tongue to be studied separately without having to consider the overall dynamics associated with a
Table 1. Source of station data used. Station
Month/year occupied
Source of data
Di 921 D i 824 D 601-D 612 G 790 -G 798 F 950-F 957
June 1932 April 1967 May 1970 January 1969
GARNER (1962) HEATH (1968) HEATH (1973) RIDGWAY(1975)
T/S relationship changing with position. The linear T/S relationship S O = roT+a, from which the anomaly is defined is that of the Subantarctic Water south of the Subtropical Convergence (Fig. 3).
Models of the diffusive-advectivebalanceat the SubtropicalConvergence
D615 •
[:)612
~.:a'.._
{///
D609
////
/
D~e
~
1155
[7o01
tI
-4"---"-" 400
I.u
/
o 1400
!i
1600
.1/"
•6 ~
Chatham Rise
220(3
240(3
0
100
200
300
400
500
km
Fig. 2.
Meridional salinity (%o) cross-section across the Subtropical Convergence at longitude 177°40'E. Isopycnals o f a t are also
shown. THE M E R I D I O N A L S A L I N I T Y D I S T R I B U T I O N NEAR THE
Subtropical Convergence indicate three distinct patterns of the isohalines:
SUBTROPICAL CONVERGENCE
Plots of the salinity anomaly across the Subtropical Convergence along 177°40'E, 179°00'E and 174°00'W are shown in Figs. 4, 5 and 6, respectively. The first two are over the zonally oriented Chatham Rise east of New Zealand--in this region the convergence has very little variation in position, being confined to the Chatham Rise, which directs the flow zonally. The other sections (Fig. 6 and at 163°50'E) are away from any immediate topographic influence, although that at 163°50'E is probably influenced by the New Zealand landmass while that at 174°00'W is immediately east of the Chatham Rise (Fig. 1). Distributions of the salinity anomaly across the
(a) a region south of the Subtropical Convergence where there is a sub-surface tongue of saline water. The distribution in this tongue is not monotonic (Figs. 5 and 6) for there are areas of significantly higher salinity imbedded in it. (b) North of the convergence a mixed layer (upper 50 m) is generally developed. The salinity in this layer decreases rapidly towards the south near the Subtropical Convergence. (c) A region below the mixed layer in mainly Subtropical Waters where the salinity decreases both towards the south and vertically downwards.
SALINITYo~
34.2 .3 .,: .5..;
.,7 ,y .~a~o.]
Relevant vertical and horizontal scales in each region for the meridional sections have been obtained by least-squares fits (Table 2). We will first test the consistency of different diffusive-advective balances with the scales of the saline tongue south of the Subtropical Convergence. The compatibility of the flow field in these models with that in the major diffusive advective balance at the convergence are then examined. The models are described by
.~ .3..4. -5 .9
tg
e,.-,
18!
So=rnT+a
17
/'/ i~/,/' D612
15
P 14 l
~
\
1|
I ~,
5 4 3 2 t
J *,/2"
'l
10
,,'/
,.,.'" ,/
8S' 8S' 82S ' 82S ' W g~ + v-= K,. + Kn
"d
f(
Fig. 3. Temperature salinity diagrams for stations on the section along longitude 177°40'E.
°
(1)
-2
-4
S~ •
~
I
. . . . . /
43 °
0612
,
';/~ f 1"1~ 1
where y is the horizontal coordinate positive to the south (i.e. essentially perpendicular to the Subtropical Convergence) with associated velocity component v; W is the vertical velocity component. Zonal changes in salinity near the Subtropical Convergence are small (see e.g. RIDGWAY, 1975) and therefore the zonal advection term u 8 S / ~ x can be ignored. 44 °
~
DeW
,' : •
o •
46 °
46 °
De06
DeOI
',.' •
l
•
•
• •
/ i
/
•
•
/
" -
S%°'75
2f
"~',~.
--
<
Surfaoe Salin~ Anorr~y
"-. I00
200
300
y(km)
Fig. 4. Meridional salinityanomaly (Too)cross-sectionacross the Subtropical Convergence at longitude 177°40PEI Plots of salinityanomaly with depth at Sta. D612 and horizontal distance are also shown.
1156
S%o 0-2 0-4 0-6
'~
42°S G?g8
43 ° G79'7 G796 GTg5
44 °G794
45° G792
G793
/
/
300
,"
400
I
,
•
:/.
•
.
.."
"
!
50~
46° G791
•
0 " 2 . ~
60(3
I !
•
J
80~
R~e
100C
'11~%.%%SalinityMaximum
S%,o0~4~I
1200
s% e4
1500
~ |
Fig. 5.
|
I
;,
.
-
20o ~w) 30Okm Meridional salinity anomaly (~oo) cross-section across the Subtropical Convergence at longitude 179~00'E. Plots of salinity anomaly with depth at Sta. G798 and horizontal distance are also shown. 43°S
s%o 0
0
"2
,
-4
•
44 °
45 °
F~I F~2
'6
•
46 °
47 °
°etF~=
48 °
R~
49 °
50 °
F~7
•
loo 2oo
/
3oo
//
4oO
/
soo ~6oo 700
/
I
/
/ I I I
0, 100o,
12o(3 •
°'6F e ' ~ , , , ° S°/oo
O'4]/
0"2 z • 0
00
Fig. 6.
SO
IO0
..Salty
%ql,~.~ Mamimum
' * / I. 50 100 150 ~ 0 k m
150
200
~0
S00
~0
400 , ~ k m
Meridional salinity anomaly (%0) cross-section across the Subtropical Convergence at longitude 174°W. Plots of salinity anomaly with depth at Sta. F951 and horizontal distance are also shown. 1157
1158
R.A. HEATH
Table 2. Observed scales and salinity anomalies and quantities derived from the diffusive-advective models Observed scales and salinity anomalies Longitude of meridional section
Vertical scale h (m) S0 exp( - Z )
Line 1 163°50'E Line 2 177'~00'E Line 3 179°00'E
Line 4 174°00'W
Region a Region b Region c Region a Region b Region c Region a Region b Region c *Region a Region b Region c
Horizontal scale L (km)
S0 e x p ( - ~ )
S0 (%o)
So (?~o)
S0 exp( - y )
400
0.18 0.50
0.19 0.38 0.38
3000 840 840
0.2
0.25
600 220
1.3
1.2
230 75 75
0.49
0.48 0.6 0.6
95 95 95
0.54 0.7 0.7
350 310 310
1,2
226 150 510
0.5 500
460
0.42 0.6
* Not well defined. Note: Region a = south of the Subtropical Convergence in the saline sub-surface tongue. Region b = in the mixed layer where the salinity decreases rapidly towards the south. Region c = below the mixed layer in mainly Subtropical Water where the salinity decreases both towards the south and vertically.
THE SUBSURFACE TONGUE OF SALINE WATER SOUTH OF THE SUBTROPICAL CONVERGENCE
It is tempting to assume that this tongue is simply associated with a vertical shear in the horizontal velocity profile. The two main components of meridional flow in this area are the geostrophic flow and Ekman drift. The relative meridional geostrophic velocity along latitude 43°S in the Pacific Ocean has been calculated using the Eltanin Cruise 28 (SCORPIO Expedition, 1969) data (Fig. 7). Also, the meridional geostrophic flow relative to 400 dbar near 43°S 149°W and 28°S 140°W has been calculated from the Eltanin stations and the meridional Ekman velocity (using a large value for the eddy viscosity
coefficient of 400 g cm- 1 s- 1) calculated from wind stress data (HIDAKA, 1958) for this locality (Fig. 8). The meridional velocities along 43°S are generally between 0 and 1 cm s-~ to the north. There is little shear in the meridional geostrophic flow at 43°S, but substantial shear both in the meridional geostrophic flow at 28°S and in the upper 100 m in the directly wind-induced flow. The depth of the turning point in the directly windinduced flow is, however, considerably shallower than the depth of the maximum salinity. Direct current measurements made by the author with two parachute drogues, one at 25 m the other at 150 m, near 43°56'S, 178°E, indicated a slow northwards meridional component with very little relative shear over a tidal cycle although there are periods of large shear within the cycle.
Models of the ditfusive-advective balance at the Subtropical Convergence
Table 2.
Continued Models of the Subtropical Convergence
Models of the salinity tongue
K,,
Horizontal scale (km) for pure diffusion, Observed values in brackets
1159
Direction of w
Direction *Iv
- - for no v horizontal diffusion
w
Horizontal diffusive and advection Kn
v
Vertical diffusive and horizontal advection
ge
Ivl
Pvl 381
(3000)
9 South
190
(230)
140
34
(95)
190
4.6 × 107 Not defined
South
Upwards
3.4 x 10 3
1 x 105
87
North
Downwards
1.2 x 10 -3
8.8 x 106
406
37
(350)
110? Not well defined
170
160
150
140
130
LONGITUDE 120
110
100
90
80
70°W
~3,5
~034 Surface Salinity along 28°S (+) and 43°S (o)
Key
qorth
X
Vo- 1500 Vo-4000 + Vo-3500 * V250-1500 •
~,,s
~ou~
*
Meridional Velocity along 43°S
Fig. 7. Meridional geostrophic flow at the surface relative to different reference levels for the leg of EItanin Cruise 28 along 43°S (SCORPIO Expedition 1969) across the Pacific Ocean. The surface salinity (%0)along latitudes 28 and 43°S are also shown.
1160
,South - 4-1'2 '
~
R.A. HEATH
-1
,
-8
•
-'6
i
4
-'2
w
i
'
Cms 0
2 !
'4
6 ;. -
-2oo
"8 -
-
'2 .
14 .
1-6 .
North 1"8 2 • ' ,
of the form s' =
)
.4oo
[I
•8oo
I
-8oo
where now the axes are such that Z = 0 along the salinity maximum which approximately coincides with an isopycnal.
I
-1000
/
I
A complete solution for S is given by the Fourier Series
•1 2 0 0 I
I
I
S = ~ DmcosmZe -k(m);,
I •2t~ °--- 1 5 ' S
rn=O
where m is an integer and k is related to m by
I
k = K~, +_ ~300
S=
o
Fig. 8. Meridional geostrophic velocities with depth relative to 3500 m between Stas. 40 (127°36.0'W)and 50 (150°35.0'W) along 43°S, and Stas. 122 (130°02.8'W) and 133 (150°51.0'W) along 28°S from EItanin Cruise 28 (SCORPIO Expedition 1969). The meridionai Ekman velocity with depth for wind stress of 0.41 dynes cm ~ at 83°T taken from HIDAKA (1958) for the region 152.5 to 137.5°W, 42.6°S is also shown.
These scant observations indicate that in the region of the saline tongue the mean meridionai flow is very weak and northwards with only slight shear in the geostrophic flow. However, shear will be frequently imposed by the directly windinduced flow. We will therefore first consider simple models with uniform flow with depth and then examine the effects of current shear. Several of the salinity profiles across the Subtropical Convergence show isolated patches of high-salinity water in this subsurface tongue (Figs. 5 and 6), which indicate horizontal transfer in this tongue is probably highly time dependent. In the models we have smoothed these patches and are looking at this smoothed salinity field.
No velocity shear
O2S' ~2S' = K . ~u y - + K~, 8Z 2'
Dm cos mZ e-k(m)~'din.
This solution can be fitted to an arbitrary salinity distribution at y = 0 which is taken as S = So exp ( - rZZ 2). Then
Dm = ~2 f f
Soexp(-r2Z2)c°smZdZ'
(e.g.p. 454, MORSEand FESHBACH, 1953), which on using the integral
fo°
e x p ( - a 2 x 2)cos bxdx = 2 a e X p
(2)
- ~
gives
Om:So J( )exp( ) and /'/1
S=SoJo
m 2'
L ~ / ~ r z ) e x p ( - ~ r 2 ) c°smZ
x exp{-yL[-1
For the case of constant flow we look for a solution to
8S'
K,, "
In integral representation this gives
kSO0 Depth(m)
v~-
Kf, + 4m2 K~J]/
+ ~ / ( 1 + 4m2KuK~'~lv2 JJ
,
Models of the diffusive-advectivebalanceat the SubtropicalConvergence For v positive the positive sign in front of the square root is taken and for v negative the negative sign. These choices allow the salinity to decrease towards the south. We will now consider different balances of equation (2).
1161
S0 ~4\
v
× exp
4(~+
(6)
Case I. No advection (v = O) Equation (3) reduces to ~.2) ~
din.
cos mZ exp
\/~]3 (4)
and the meridional flow is southwards. Again we wish to compare the horizontal scale of this solution with that observed in the tongue. On the 1' axis (Z = 0) we have S
1
We wish to compare the horizontal scale of this solution with that observed in the tongue. On the y axis (Z = 0), equation (4) gives Using the horizontal scales L = y, where (S/So) = e- 1 gives values of K~/v ranging from 9 to 37 for the first three lines (Table 2). Unless the meridional velocity is remarkably small (~0.05 cm s- 1) the sizes of these vertical diffusion coefficients are very which has a solution (ERD•LYI, MAGNUS, much larger than the typical upper values of OBERHETLINGESand TRICOMI, 1954, p. 146) 1 cm 2 s- 1. This would indicate that the balance in this tongue is not simply between vertical diffusion S= So exp(rZy z K~) and horizontal advection. Further, if horizontal diffusion is included and the flow is still towards ×[1-2g-a/2forY~(~)exp(-t2)]dt. (5) the south the vertical diffusion coefficient would need to be still larger. The horizontal scales L[S=Soexp(-y/L)] evaluated from equation (5) for three of the lines Case 3. Vertical and horizontal diffusion, horizonusing a value of (Ku/K~) = 106 are given in Table tal northwards advection 2. On the sections over the Chatham Rise these Equation (3) was integrated numerically, using horizontal scales are close to those observed. For the adaptive Simpson method using interval bisecthe section away from the constraining influences tion (e.g. MCKEEMAN, 1962). The values of Kdv, of the Chatham Rise (lines 1 to 4) the horizontal Ku/v and r were varied and S/So computed at scale is substantially less than that observed, different positions (Z, y). The horizontal exponenindicating that here probably horizontal advectial scale e x p [ - (x/L)] calculated from these disttion has a strong influence. ributions for various ranges of parameters is given in Table 3. For the range of vertical scales of Case 2. No horizontal diffusion (K n = O) interest here, exceedingly large values of K,,/v are Equation (3) reduces to needed before vertical diffusion plays a role in determining the horizontal scale. Also, the vertical S = S o /' 1 cosmZ scale is constant along the tongue. Alternatively, the vertical scales need to be very small before vertical diffusion, with acceptable values of K jr, x exp - m 2 + 4rfi dm plays a role in determining the horizontal scale.
×foeXpl-m~/(~--~)Y-4F]din'
1162
R.A. HEATH
Table 3, Values of the horizontal exponential scale 7 calculated by numerical integration of S
,~,
1
~/( 1 + 4m2KnK~)]/ 2Kndm : )31 K,.
×exp(-YV][-l±
\
K,,)I_
K o K~ i for different values o f - - , - - and r = - - . v v H
H
K~,
Kn
?
(m)
-v (cm)
-v (cm)
(kin)
75-500 75-500 75-500 75-500 75-500
0.1 0.1 0.1 0.1 0.1
---, 3.2 ~ 3.2 ~ 3.2 ~ 3.2 ~ 3.2
2× 4× 8× 16 × 32 ×
106 106 106 106 106
20 40 80 160 320
The model gives acceptable values of Kn/v between l0 T and 3 x 108 cm, the values being greatest on the lines away from the restraining influence of the Chatham Rise. Velocity shear To examine the effect of velocity shear we can express the meridional velocity as a constant Vo and a component varying with depth v(Z), i.e. ~S'
~2S'
~2S'
{Vo + v ( Z ) ] - ~ - = K n ~3y - 2 + K~ OZ 2 " cy A solution of this equation of the form S = So e -ty e -ky(z~ exists if K n 12
I f " t Z ) - ,--~-[Vo + V(Z)]
Kv k
kf'(Z) 2 = O,
where Vo is chosen such that where (O2S/OZ2) = v(Z) = 0, v = v0. The horizontal scale then is determined by Kn/v in a similar manner to case 3 above. However, the vertical salinity distribution is determined by the current shear and vertical diffusion. For a realistic difference in wind drift of 0.01 m s- ~ over the top 100 m the vertical diffusion coefficients for the observed vertical scales of the first three lines are 0.07, 1.1, 1.4cmZs -1, respectively. Alternatively, the geostrophically observed difference in speed in the upper 100 m on line 2 of 0.005ms-1 gives a vertical diffusion coefficient of 0.6 cm 2 s- a on that line. The balance in the sub-surface saline tongue appears to exist between slow northward advection and both horizontal and vertical diffusion with the vertical scale being determined by slight shear in the horizontal flow and vertical diffusion. We wish then to consider the compatibility of this proposed meridional circulation with the major balance at the Subtropical Convergence. D I F F U S I V E - A D V E C T I V E BALANCE AT THE SUBTROPICAL CONVERGENCE
North of the Subtropical Convergence the geostrophic meridional flow is towards the south (see e.g. Fig. 8). However, the latitude of zero zonal wind stress is about 35°S (HELLERMAN, 1967) which is generally north of the latitude of the Subtropical Convergence (DEACON, 1945, Fig. 4). Therefore the meridional component of the surface wind drift at the convergence will be towards the north. Within the mixed layer at the Subtropical Convergence the probable advective diffusive balance is between horizontal advection and diffusion described by ~S' c~2S' V~y = K H Oy2
which gives
Kn
-
[-
1
V0
and
The horizontal profile appears to be exponential in form with a simple solution S = S'o e - ylL,
kKv v(Z) = [ f " ( Z ) - k f ' ( Z ) z] - l '
where L = (g./Ivl) for v which must be towards the north. The values of Kn/Ivl for the four sections
Models of the diffusive-advective balance at the Subtropical Convergence
are given in Table 2. They range from 7.5 to 3.1 × 107 cm, being smallest where the convergence is confined to the Chatham Rise which is where the meridional flow would probably be least. Below the mixed layer at the Subtropical Convergence the isopycnals slope sharply upwards (Fig. 2), and the balance would appear to involve both horizontal and vertical advection and diffusion, described by 8S'
W~
8S'
+ v
cY
82S '
= Kn
~
(~2S'
+ K,,
~Z 2 •
Both the horizontal and vertical profiles decay approximately exponentially and a solution with constant flow is s' = So e -pr e -jz,
(7)
where -pv-jW
= Knp 2 + K~f .
In lines (1, 2 and 4) the meridional flow will be towards the south, thus the vertical flow must be upwards. However, in the region of line 3 the meridional flow was northwards (Fig. 1, HEATH, 1973). A crude estimate of the ratio of vertical to meridional flow is given by the slope of the isopycnals, assuming the flow is essentially along isopycnals and the zonal change in properties is small. This gives value of 1 to 3× 10-3cms -~ (Table 2), values which as expected are large compared with the typical downward vertical velocity of 1 to 5 × l0 -4 cm s- x below the frictional layer, which is required to balance the curl of the wind stress. Substitution of the scales in equation (7) shows that the role of vertical diffusion in this region is small compared with horizontal diffusion (Table 2).
DISCUSSION
In brief the meridional circulation at the Subtropical Convergence over the Chatham Rise appears to consist of northwards flow in the mixed layer with southwards and upwards flow below. This is consistent with the limited available current observations and simple diffusive-advective balances, horizontal advection and diffusion in the
1163
mixed layer, and mainly horizontal diffusion and horizontal and vertical advection below the mixed layers. The balance in the saline tongue extending south from the Subtropical Convergence is mainly between horizontal diffusion and northwards advection, with the vertical scale being determined by weak shear in the horizontal flow (parabolic in form in the model with the slowest flow at the axis of the tongue) and vertical diffusion. No attempt has been made to match together the three distinct distributions, for the process is obviously very complex. However, it would appear that the tongue is generated at the Subtropical Convergence by the shear in the upper few 100 m. Accepting the meridional circulation as proposed above the balances give values of Kn/v of 10 6 to 108cm, values which are in the range of those found in other studies (e.g. HAN-HSlUNG a n d VERONIS, 1970; NEEDLERand HEATH, 1975). The balances, however, do not allow the size of K d v to be established in any detail. Acknowledgements The author would like to thank Dr A. E. GILMOUR of the New Zealand Oceanographic Institute, D.S.I.R. for helpful discussion and Dr R. WOODING, Applied Mathematics Division, D.S.I.R. for help with the numerical integration computation.
REFERENCES DEACON G. E. R. (1937) Hydrology of the Southern Ocean. "'Discovery" Reports, 15, 1-124. DEACON G. E. R. (1945) Water circulation and surface boundaries in the oceans. Quarterly Journal of the Royal Meteorological Society, 71, 11-23. ERDI~LY1A., W. MAGNUS, F. OBERHETL1NGESand F. TRICOM] (1954) Table of integral transforms, McGraw-Hill, Vol. 1,391 PP. GARNER D. M. (1959) The Subtropical Convergence in New Zealand surface waters. New Zealand Journal of Geoloyy and Geophysics, 2, 315-337. GARNER D. M. (1962) Analysis of hydrological o bservations in the New Zealand region 1874-1955. Memoirs. New Zealand
Oceanographic Institute 9. (Bulletin of the New Zealand Department of Scientific and Industrial Research 144.) GORDON A. L. (1971) Oceanography of Antarctic waters. In: Antarctic oceano#raphy, I. J. L. REID, editor, Antarctic Research Series Vol. 15, pp. 169-203. HAN-HsIUNG K. and G. VERONIS(1970) Distribution of tracers in the deep oceans of the world. Deep-Sea Research, 17, 29-46. HEATH R. A. (1968) Geostrophic currents derived from oceanic
[164
R.A. HEATH
density measurements north and south of the Subtropical Convergence east of New Zealand. New Zealand Journal of Marine and Freshwater Research, 2, 659-677. HEATH R. A. (1973) Direct velocity measurements of coastal currents around the southern half of New Zealand. New
Zealand Journal ~f Marine and Freshwater Research 7, 331 367. HELLERMANS. (1967) An updated estimate of the wind stress on the world ocean. Monthly Weather Review, 95(a), 607 626. HIl~AKA R. (1958) Computation of the wind stresses over the oceans. Records of Oceanographic Works in Japan, 4, 77- 123. MCKEEMAN W. M. (1962) Algorithm 145' adaptive numerical integration by Simpson's rule. Communications. Association ./or Computing Machinery, 5, 604.
MORSE P. M. and H. FESHBACH (1953) Methods of theoretical physics, McGraw-Hill, 1978 pp. NEEDLER G. T. and R. A. HEATH (1975) Diffusion coefficients calculated from the Mediterranean salinity anomaly in the North Atlantic Ocean. Journal ~/ Physieal Oeeanoqraphy, 5, 173 182. RIDGWAYN. M. (1975) Hydrology of the Bounty Island region. Memoirs. New Zealand Oceanographic Institute, 75. SCORPIO EXPEDITION (1969) Physical and chemical data from the SCORPIO Expedition in the South Pacific Ocean, Scripps Institution of Oceanography Reference 69-15. Woods Hole Oceanographic Institution Reference 69-56. SVERDRUP H. U., M. W. JOHNSON and R. H. FLEMING (1942)
The oceans: their physics, chemistry and general biology, Prentice-Hall, 1087 pp.