FISHERIES AND MARINE SERVICE

Translation Series No. 3213

T S analysis of waters in the world ocean

by 0.1. Mamaev

Original title: T,S - Analiz vod mirovogo okeana

From: (Unknown),. . 272-291, 1970

Translated by the Translation Bureau(GRL)Multilingual Services Division

Department of the Secretary of State of Canada

Department of the Environment

Fisheries and Marine ServiceMarine Ecology Laboratory

Dartmouth, N.A.

1974

29 pages typescript

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UNEDITM TRANSLATION

F o r i rArgmeii-s, n orRy T—S ./..LUALYSIS OF WTLRS OF TEL WORLD OCLI,,N

TRADUCTION NON REVISEE

By 0.1. Namaev inforrna'iion -,r,euteeiletit

Lomonosov Moscow State .University Department of Geography, • Chair of Oceanology

The limitation formulated above regarding the mixing of waters 272û

inA in B in different proportions, ----=.--- , is artificial, but from the

1nD Inc

oceanographic point of view it seems reasonable. Actually, by examining

the position of the quadrangle ABCD in the field of the isopycnals

we can see that the position of the surfaces of equal percentage

content of waters, along which "horizontal" intermixing is assumed to

take place, corresponds quite closely with the position of the isopycnic

surfaces. Thus, the principle of isopycnic intermixing is more or less

,confirmed..

The study of vertical and isopycnic mixing of four water masses

is most rewarding in regions of significant horizontal gradients of the

oceanoloeical characteristics, in particular in "transitional" (after

Sverdrup) and frontal regions. The nomogram proposed above (Fig. 6.21)

was used by V.V. Natarov for studying the intermixing of water masses over

the continental slope of the Bering Sea..

ù Numbers in the right-hand margin indicate the corresponding pages in . the original..

SOS-200-10-31

2

Sec. 48. . INCREAJES IN DLUSITY RESULTING PRO M THE VERTICAL MIXING OF WATI.:11 MASSES. TRIANULES OF INCREASE IN DENSITY (CONTRACTION) on mixilq.

We have already dealt with the problem of the increase in density

on mixing from the point of view of the anomalous properties of sea water,

and also from the standpoint of the general theory of T-S diagrams (Sec..

30). An accurate method of computing the increase in density was con-

sidered there, based upon an estimate of the curvilinear integral along a

T-S curve. In this and the folluldng sections we return again to this

problem, but from the purely oceanographic standpoint: namely, me shall

examine a general method of computing the increase in density on mixing,

and also the problem of the manner in mhich the increase in density on

mixing influences the transformation of water masses of the ocean.

It is well knomn that only a few works have been devoted to the

investigation of the increase in density resulting from the mixing of waters

under actual conditions in the world ocean. It has already been mentioned

that from the oceanological point of view the phenomenon of the increase

in density on mixing was studied in mOst detail by N.N. Zubov (1938, 1947,

1957b)c, McLellan (1957) studied the influence of the increase in density

on mixing on the interaction of the waters of the Gulf Stream and the

Labrador Current,. Fofonoff (1956) - its influence on the formation of the-

antarctic,bottommater mass in the region of the Weddell Sea, and V.A.,

Bubnov (1960) - on the mixing of the waters of the Kuroshio and Oyashio..

The author (Mamaev, 1960) investigated the influence of the increase in den-

sity on mixing on the transformation of the intermediate , mater masses of ,

the ocean using as an example. the Mediterranean intermediate mater mass:

in the Atlantic Ocean;.Namaev (1963) proposed a "triangle of increase in

3

density (contraction)" which has proved to be very convenient for deter-

mining the increase in density on mixing from the T-S curves. Problems

touched upon in the above-mentioned works of the author, namely, the

problem of the use of triangles of contraction on mixing, and the problem

of the influence of the density increase on mixing on the transformation

of the Mediterranean intermediate water mass in the Atlantic, were de-

veloped further in the works of KinIdyushev (1965) and Bubnov (1967). The

triangle of contraction on mixing was used by Dubrovin for determining

the lowering of the sea level resulting from the .increase in density on

mixing in the region of interaction of the waters of the Gulf Stream and

the Labrador Current. Finally, the author (Mamaev, 1969c) investigated

the problem of the ilcrease in density on'mixing of four water masses of

the ocean; this is discussed below, in Sec. 50..

Problems of the methods of computing the increase in density on

mixing, mainly of tmo mater masses, and its influence on various oceano-

logical processes were investigated in detail in the work of N.N. Zubov

and K.D. Sabinin (1958), and therefore we shall not deal with details dis-

cussed in that work, but shall devote our attention to problems outside its

frame of reference, namely, as already stated above, mainly to problems

related to the increase in density resulting from the mixing of three and

four water masses, and also to the horizontal (isopycnic) mixing of strati-

fied mater masses in the ocean. The problem of the mixing of tmo water

masses, described by Zubov and Sabinin,is a sort of preamble to the sub-

sequent discussion..

Mixing of t w. o water masses. In Sec. 16

we examined the mixing of different parts of tmo mater masses.. In the

-!- a in i ni2 • (48.4)

•

Ap (48.5)

4

case where two water masses mix in different proportions the average

temperature and salinity are computed from the mixing formulas (24.1) and

(24.2), while the increase in density on mixing-Lpis determined from

the formula.

. !1«?-----P ( T, 79) (48.1)

where e(57, 7$) is the density of the mixture, and (5 * is the mean density,

determined from the formula analogous to the mixing formula

Q1Pi Q.-) 5 2 p — Q 2

(Q is the volume). The value

\ rer, — a (27, ,§)

(48.2)

(48.3)

may be called the contraction on mixing; here a is calculated from 274

the formula

where m is the mass.

Values of the increase in density Acf and the contraction Aa..

differ in sign but are very close numerically (see formula (17.16))

The difference between the increase in density on mixing and

contraction on mixing was emphasized by K.D. Sabinin (Zubov and t5abinin,

1958); incidentally, in the English literature (Fofonoff, 1956) used the

second term (contraction on mixing). Sabinin also showed that in the

* This should surely be sigma (a)? - Transi.

5

computation of the average values of j5 and a from the mixing formulas,

volume proportions must be used in the first case, and mass proportions in

the second case.

On further examination of the mixing curve depicted in Fiô. 2.5,

we can see that by dividing it into 100 parts, we can determine the

densities (specific volumes) of T-S points, corresponding to aSiven

volume percentage of the two water masses; then, by computing 15 and Y

the increase in density or the contraction can be determined.. The corre-

sponding coiaputation:-'or the water masses of the Gulf Stream and the

Labrador Current .is presented in Table 10..

To6ntu{a 10

2

Table 10.

Z Pavier ynlorxe:+na np,,i c»ee:eHiMi r• p33a11411tiix nponopttnAx so,:kxax .riacci'oae;)crpnata (A) it .'taSpa,:kopcKoro -re^tefn;u (L)

a^ so^uA

?oL

^ T^

S o, , (T' •

yaT

5 '1 6^

75 8 6 97 8 1.C

100 0 30,00 33 ,33 22,02 2'?,0•3 .^ 0 0U 10 26,8 .5 ^731,: ?^, ;^i 2.^,02 0,_l.l -0,4480 2 0

_27 , 7 0

_33,I7 22,81 '2-1,02 0,79 -0,/9

70 30 ' ?0,'3 32,97 '23,00 ??,0'3 1,Oî -1.0760 40 17,40 3'2,17 23,23 • 22,02 126 -1 2550 50 1.1,2.5 31,35 23,3S ?l,0•3 1,,55 -1,5.540 60 11,10 30,5 S 23,36 23,02 1,3-1 -1,3430 70 7,95 29,75 23,22 ?->,0? 1,_:0 -1,2020 80 4,S0 28,^JS . 2_?,9F 22,02 .0,9•1 -0,9^10 90

.l',G7' 2S ,15 ?'?,5G 22,03 0,:r1

• 0 100 --1,50_

2r,35 22,02 22,02 1 0 0

1. Co ;Mnutation of the increase in density on mixing of water masses of the

Gulf Stream (L) and the Labrador Current (L) in different proportions.

2.. ,, wz. te.r3. ::,.tp l^:nation of Table 10

A., Coltrnn 1. - pcrcentaLTe of water x5. Co7_LLZn 2* - perccnt« - e of water Z6. C^l.u^nn 3 And Co^lu^:1n4 - values of. the temperature and salinity

on mi-xin^ of w^3ter masses k and L in the proportions indicated

;

6

in Columns 1 and 2. They were calculated according to formulae (24.1) and (24.2);

7. Column 5 — O-- (T, :c7) — density of the mixture.- It was taken from the T-S diagram from the corresponding T-5 points;

8.. Column 6 — ar •.* average density. It was determined from formula (48.2);

9. Column 7 - increase in density on mixing, A.a ,..„, a7.0.:à; 10.. Column 8 - contraction on mixing, Ach.-àur.

In the above exLmple the densities of both initial water masses

were identiéal; it is obvious, however, that the computation of the dncrease

in density would be the same if their densities are different. In Fig.,

6.22 are depicted the density curves of two mixtures which are formed when

one and the same water mass B (index T ,..= 2.5°0 ; 34.90%0) is mixed in

different proportions either with water mass A (index T ==12.50C ; 5==

35.67%0), or with wa ter massll (index T= 11.90C ; 3=35.50%e). This

figure is the result of computations completely similar to those cited in

Table 10.

o

Fig. 6.22

100 80 60 40. 20 70C0a.9où elaccu 2

Puc. 6.22. Kpunble ynaoTnegnn ripa cme-

weggn Tio.LII0Çt maccsi B c rso.D.limmu ac- I nia M.

Curves of.the increas'e in density resulting from the mixing of - water mass B with water masses A and M.

2.. % water mass B

7

M i x i n g o f t h r e e w a t e r m a s s e s. The

increase in density /.^p or contraction -/-\CY resulting 'from the mixing of

three water masses is determined from the same formulas (48.1) and (48.3),

except that here P. and GY refer to weighteu^.i^as.n v6l..iihs cif:': t i:6;°density or

specific volume, which are determined from the mixing formulas of three

ttira.ter masses:

- ; Qt et ' Q ^-2 O'?-., -^

-i- ut.jz,x =- --= .

(48.6)

It is recommended that trian,,les of i.ncrease in c,e^ be con-

structed for determining the increase in density (contraction) on mixing,

corresponding to a given percentage proportion of the three water masses

being mixed, which is determined by the position of the corresponding

point within the mixing triangle. Let us illustrate the principle of

such a construction by the example of a mixing triangle for three water

masses having the following T-S indices:

Water mass A: T = 12.5°C ; S- 35.67^^0;

Water mass Tf: T = 11.9°C ; S=- 36, 50i^0;

Water mass B: T= 2-50C ; S=34, 9M%0.

These three water masses correspond to the Atlantic surface water

mass in the Azores-Pyrenees region, the intermedï,ate Mediterranean water

mass and the deep and bottom Atlantic water mass (Mamaev, 1960b) . The

corresponding mixing triangle is depicted in Fig. 4.2. It is apparent

that these three water masses are in a state of vertical mixing.

For the construction of a triansle of increase in density the

following steps are necessary :.

1. Values of and cx are computed from formulas (24.1) and

We shall discuss the contraction on m.ixing:, below.

(24.:'), and also frour:formUla (48.6) for all points in which the per-

centage of each of the water masses is a multiple of 10%; these points

are numbered from 1 to 66 in Fig. 4.2.

These computations are conveniently summarized in a general

table, making it possible to abbreviate the computations considerably;

inasmuch as the form of this table is arbitrary, we shall not cite it,

but shall limit ourselves to an example of the computation of one of the

points, namely, No. 16, where the proportions of the water masses 4 II

and B amount to 10, 40 and 50%respectively (Fig. 4.2):

........ ....._ . 10 + 11 ,9 • 40 +2,5 ' 50 — 7,26'.

... . .. _ .1., ==. TAin .4 + Tlim.11 + T rin/ B _ 12,5 •

100 " 10.0 S in i + S i ,in, r + .9„inz2 _

.

8

.-

100

35.57 • 10 + 36,50 + À90.50 109 •

vAnz A ± twez if vfin1,3 V 2.

100 ==

73,6S 10 + 72,95 + 72,SS • 50 109 =72,99.

2, From the T-S diagram the potential specific volumes,

/./:t7 g), where nr.= 1, 2, ... , 66, are determined from average values of

the temperatures and salinities "rand g for all 66 points Of the triangle.

For point No. 16 we have: v(T, S)== 72.86.

Values of the contraction L. -0 also are determined from formula

(48.3) for all 66 points of the triangle. In our example 2.e . Vijn72.86--

72.99 ===--0.13. For the three sides of the mixing triangle Bi, AM and

MB the values of the contraction on mixing, determined in a similar manner,

are presented in Table 11.

9

Ta6..eutia 1.1 . •

1 Cx“urite - 10 5

2 CTopoira TpeyroobintKa BA .

1■".9 . . . . 1 • 12 22 31 39 46 52 57 61 64 66. Au . . . . . . 0' 3 8 11 13 13 13 12 . 9 2 0,

• Cropon Tpeyro.-itilim:a AM

1S2 totie;: . . . 66 65 63 GO 56 51 45 38 30 21 11 - 0 0 0 . 0 0 0 1 1 0 0 O.

CTopoila Tpeyroablma MB • • • •

TorteK 11 10 9 - 8 76 5 4 3 2 1 Au 0 5 7 12 13 13 12 10 8 4 0•

Table 11 -

1, Contraction on mixing -Ay 005

2. Side of triangle 3. Point No,

It can be seen from this table that the contraction on mixing

is quite insignificant on the side AM; it is much greater on the sides

and MB, while the values are very close at the ends of the straight

lines 2-12, 3,-22, 4,-31, , 10,-64, which are parallel to the side

AM.

3.. Curves of increase in density on mixing are pletted for lines

on which all the points are observed to have the same percentage content

of one of the water masses. In the example in question, the lines

selected were BM and lines parallel to it, on which were observed 0, 10,

20, , 90f., content of water mass A.

In Fig. 6.23 are depicted curves of contraction on mixing for

lines on which the percentaje content of water mass A amounts to 0 (line

BM), 20, 40, 60 and 80. In plotting the curves of increase in density,

the scatter of individual points, caused by inaccuracy in the computation

10

of the increase in density^is smoothed out (this inaccuracy can be

avoided by computing -2) or d_ to the third decimal place instead of to

the second).,

l+. A triangle of increase in density (contraction) on mixing is

constructed. In the present case of the vertical mixir; of water masses

A, Pi and B, the triangle of contraction on mixing is depicted in Fig.

6a2/., In -F,his example the construction of the trian;le of contraction 278

proved to be simple; actually, by referrin,^ to Table 3.1, we can see that

the contraction on mixing at the ends of lines paralled to the side AM

does not differ by more than !S ?i =--2.10-5. By neglecting this difference

and also asstuning that the contraction on mixing of water masses A and M is

equaJ. to zero, we plotted isolines of contraction on mixing parallel to

the side >YtM.. Actually the picture may be more complicated.

This completes the construction of the triangle of increase in

density (contraction). By plotting on this triangle the T-S curves of

individual oceanological stations, we can evaluate the magnitude of the

influence of the increase in density on mixing, which is inherent in

nature, on the process of vertical intermixing of three water masses. As

an example, in the same Fig. 6.2/+ is depicted the T-S curve of,-,station

225, occupied by the E};padition Ship "Mi lshail_ Lomomosov" on the 16 October,

1958 at the coordinates: t^ =470 l^i/+6.2'N,, .,` =170 14-31 W. On exznina-

tion of this T-S curve we see that the contraction on mixing reaches its

greatest value (---13.10-5) at the lower boundary of the intermediate

l.-editerranfeail -va ter mass 14 m).. The. influence of contraction

on mixing i roduces an uneven type of mixin;.; of the three water masses, and

especially a hi,.I,her rate of mixin;Y of water mass M with water mass B, than

11

-10 5iSCt

• 15 là

5 !tilt! I t

1 2 3 4 5 6 7 8 9 10 II

t t 1 1 1 1 1 IN

22 24 26 28 30 •

52 54 56 .

61 62. 63

Fig. 6.23

Fite. 6.23. I■lpuBble c:4ZaTM Bryn cmelucultll COOTECT-

CIT.y10111MX 0,20.40, GO it $.0-npo- null- Homy ccuep -,-KaBlr:o BoaBoit maccbt ii B Tp1yrO.ThHIiEe cme-utelma, - u3o6paxzeu1tom imc. 4.2.

•

Curves of contraction on mixing for lines corresponding to 0, 20, 40, 60 and 80 percentage content of water mass A in the mixing tri-angle depicted in Fig. 4.2.

with water mass A. This.problem is discussed in more detail below in Sec.

56 in connection with the transformation of the Mediterranean water mass

in the Atlantic; this model has been investigated the most, as already

mentioned above, and therefore we are devoting a separate section to it...

The application of the triangle of contraction on mixing to the

analysis of individual T-S curves makes it possible also to plot curves

of the vertical distribution of the contraction on mixing, Acx==h7:),

for each individual station. Such curves, for example are presented in

the study of V.I. Kintdyushev (1965).

12

rec . .5

10

36.0

A ?SO

200 • 300

403 500

600 00

SOO

11

2000/,,, -_,2,--d

2564(:-.7 ..kli72- 4

3500 e.: a

•

-

1 I

35.5 t • t

36.5 SX0

0 , , • 35.0

Pv.e. 6.24. t:;.);t tzo ....;apx:r.perttoît (A), (.'1) it r.-tytalloft It npv...:koitticlit CCLIDO.

P..T....atrrnec.:.o.il • (8) mitcc, z1Tae„,c. 7', .S-;se c -raiii.ura 225 IC «M t in ;Li II omoiloco 3».

Fig.. 6.24 Triangle of contraction on mixing of Atlantic surface (A)

Mediterranean intermediate (M) and North Atlantic deep and bottom (B) water masses, and also thé T-S curves of station 225, Scientific Research Ship "Mikhail Lomonosov".

As previously mentioned, the triangle of increase in density on

mixing depicted in Fig., 6.24 is very simple, but for other regions of

the ocean it may prove to be more complicated. For an illustration of

this we cEm refer to Fig. 6.25, on which is shown the triangle of increase

in density (contraction) resultin from the mixin of subarctic, equatorial

and deep water masses of tne j.'cific Ocean. The use of this trianble 280

for the analysis of the processes of intermIx1u; of wt.ter musses is dis-

cussed in the followin section.

_ 14 _

?

/ 111111720

24 26

le 14

• •

cr

p 1.14 /

-7/20 ie /6

. •

13

It should be pointed out that the influence of the contracti,q

bility of sea ynter, which has been disregarded in both the T-S analysis

and in the analysis of the increase in density which occurs in the vertical

mixing of water masses, requires further investigation; this may intro-

duce considernble corrections into what has been described above..

4 6,— .1

Pn. 6.25. Tpcyro.ibutn; c4aTn nplr cmelmelum (-10 5 Acz) norlepTHIA cy& • apialltice::oft liOPUNI:OCTi:011 bi-maropuna.Litoii (C) i r.-iy6uHnoi: (B) , so.rutux •

• macc comepHoil T/IX01 o cyzeana. •

Fig. 6.25. Triangle of contraction on mixing (-10 5 Acl) of subarctic sur-

face (A), equatorial surface (0) and deep (B) wa ter masses of the northern part of the Pacific Ocean.

Sec , 49. INORLASL IN DENSITY RLSULTIN.IT' FRON rfa HORIZONTAL NIXING OF "WATER MASSES.

The horizontal mixirg of ty,c) (three) water masses, -which differ

considerably in regard to their T-S characteristics, has been observed,

as already nentioned (Sec. 46), principally in frontal regions of the world

ocean. The most impressive example of such mixing is the interaction of

the water masses of the Gulf Stream and the Labrador Current; we have al-

ready dwelt on this example above (Sec. 46) and now we shall return to it

again,

14

It is well knôim that the interaction of these two water 'masses .

A and L results in the formtion of the product of their mixing thè

specific va ter mass of the continental. a^ione (SL). The, increase •ind.en-

sity on r.iix-ins exerts a si^;nif. i c,-^nt influence on the forTia.tion of this

water mass. This t-,-as studied by N.N.IZubov (1957b) and. also by McLellan

(1957). Let us consider the influence of the increase in density on mix-

ing on the horizontal inter;lixin;^ of the water masses of the Gulf Stream

and the Labrador Current. In Fi^. 6.26 are depii!ibc: I the T-S curves of

the ix-aters of the Gulf Strewn, the Labrador Current and the product of

their mixing -- the water mass of the continental slope. i4cLellan, and

likewise Tibby (194•1) , made the assumption that mixing takes place between

water masses of the same density: for example, Labrador water, which is

represented by point a in the figure, mixes with Gulf Stream •v^^ter b

, ^/so

4t, ^^^ 11,0

400I

27,5 -

/

riltu ?8,0

600

• ^tco^ Y/

«^

^ ^ ,

d C"i ^^-- --^ 7 ^

T°

16

• 12

to

8

6

4

2

o

3+ 35

Pi;c. 6.2G. !;):,c^l!; iec,oc u« r.; te ;e!«!e VI:.; OT:'.CI!i!S «pu cueiuc«««ro T , .S•q?ilsLUl iC.:i!^L: )I^CC rO.IL 1CTi^11.`.f1 (;l) It .7.i;Üpa;IOU-

-Ci•TZ4C:Ii!)i (1.^. iÎi!:P,fCO?.i J.j. OûoS:a1!c:ila l9^1Sf >11CC

p:[noaoro cl<.-Irma (Mc Lellan, 1957).

281

15

Fig.. 6.,-,-6Graphical determination of the increase in density on mixin^

from the T-S curves of the vater masses of the Gulf Stream (LO and theLabrador Current W. The index SL indicates the T-•5 curve of the conti--nental slope (14cLellan, 1957).

where ( e<r ),y = (c^-r)j) -27..00.. Because the nature of the mixing

process deviates from isopycnic inixin;; (the product of mixing does not

lie on the isoline 0;=27.00, but on the stra.ioht line E7^ ), the in-

fluence of the increase in density shows. Products of the mixing of the

two initial water masses are represented by points which lie on the T-S

curve of the ,:ater mass of the continental slope of the ocean and on the

correspondiny mixing lines; the point C represents the product of the

mixing of i•iaters ci and 6, the point •f repr. esents the product of the mixing

of waters d and e, and so on. The computation of the increase in density

on m i.xin; in this c^Ese is illustrated in Table 1.2. We c^zn see from this

table that the hiEhest value .d cr, `:.0.17 of the increase in density is

reached on the isopycnic surface dr = 27.00^ These values remain high in

the upper lLyers but decrçase with the depth. Thus, as also in the case 282

of vertical mixing of v,ater masses, the increase in density on mixing

reaches its highest values somewhere at intermediate depths. This very

interesting phenomenon requires additional diligent investigation.

In an investigation of the horizontal interaction of three water

masses the problem of studyin-, the increase in density on mixing also

requires the construction of a triangle of contraction on mixing; more-

over, the foamnal side of the probl.em, and especially the construction

itse:i..f of the triangle of contr"ction, is the same whether we are study-

in; the. vertical or the horizontal interaction. of the waters. Differences

in the processes of interaction will appear withiii'the tria.rigl.e 'of -

xx 'l'ranslator.•'s note; The value 27.60 in the Russian text is apparently atypographical error.

5

16

contraction after we begin to examine real T-S relationships, plotted

either according to the parameter Z , or the parameter./

TaCmutia 12

YIUTOTHelllie 11 1 111 ropn3oulanknom cmcinennu tioikumx mace rœiLdiclimma n Jlaiipuopckoro Tegeinin, no MaKaconany (McLellan, 1037)

2'..... •

ro..114CTIMM .1,M/ 3110 M:0 e B oana g mac4à marcruEonoro cx.leita • Teuune

.L •

e u --- o ...

• - • 9 g n

T `C S °/ reC $C14) T `C S ''.ica CT i-.. 6

26,8 14,50 35,92 --0,80 33,30 10,48 35,23 27,07 0,09 74 26,9 13,30 35,72 -0,68 33,43 9,95 35,17 27,11 0,12 76 27,0 12,20 35,55 --0,42 33,57 9,42 35,12 27,17 0,17 78 27,1 11,0S 35,41 0,06 33,73 9,00 35,09 27,21 0,11 SI 27,2 9,93 35,27 0,65 33,00 8,43 35,05 27,26 0,06 84 27,3 8,90 35,18 1.20 34.07 7,81 35,03 27,33 0,03 86 27,4 7,88 33,12 1,78 31.24 7,10 55,01 27,43 0,03 3 7 27,4 7,02, 35,0 3 2,36. 34,42 6,40 34,99 27,52 0,02 . 37 27,6 . 6,10' , 35,04 2,90 34;61 '5,60 34,98 27,61 0,01 . 86

Table 12.

1. Increase in density resulting from the horizontal mixing of the water masses. of the Gulf Stream and the Labrador Current, after McLellan (1957)

2. Gulf Stream 3. Labrador Current. 4. Water mass of the continental slope 5. Initial value of 6.. increase in density 7. Percentage content of wàter masses of the Gulf Stream

In considering the nature of the increase in density resulting

from both the herizontal and vertical mixing of waters, let us return to

the case of the interaction discussed in Sec. 46, of the subarctic (0,

deep (B) and eouatorial (C) water masses of the northern part of the.

'acific Ocean. The computation of vertical mixing with an underlying

water mass also introduces corrections into the picture of the inprease

in density, as can be seen from Fig. 6.25, in which the corresponding •

ca.

:›■

a P 2

›

a •

a

a

•

3

4 6 8 10 (2 ! /6 19 20 -22

rny.50H,o,p sci.?Ncy aracca fee nagu2cini 8 • •

Pcc. 6.27. Ibo.-Ininnt CMCWeitil!: nOs;:pxHZCTHoà cyt5apKTmqeO:i (A), . . _ _ .

1107.epX1raccii0i; (C) n ray6nn- nofi (Li) ce3epo-isoCTO4uea 1'FiX0ro e::e2:ia na ye.-.oalom pn3pc3e: itIrpnxo-nofi .-utan-zfi iianecno 307:,-noe

nol't maccbc C.

17

triangle of contraction on mixing is depicted, and Fig. 6.27, in which

the isolines of contraction on mixing are shown in an arbitrary cross section

(compare with Fig. 6.15). The values of the increase in density, which 283

served as the basis for plotting the isolines in Fig. 6.27, were computed

for all points of the square grid in Fig. 6115 (ei[cepting the line BB 1

we have 110 points) according to the method described for the construction

of "triangles of increase in density".

Examination of Figures 6.25 and 6.27 shows.us that the increase

in density resulting from the mixing of -water masses A and B is practically

Fig. 6.27 1, Isolines of contraction on mixing (-10 5 ci) of surface subarctic surface equatorial (C) and deep (B) water masses of the northeastern

part of the Pacific Oce:- n on an arbitrary cross-section. The 50;:; content • of water mass C is repreented by the daned line.

2. Subarctic strucLur 3. Lquatoril struct•,,tre 4 , Deep ater mass of the Ecrth Pacific.

18

insignificant; maximum values are not reached in the horizontal mixing

of waters A and C, but in the vertical mixing of waters C and B. The

region of maximum values of the increase in density, as mould be expected,

is close to the isoline of the 50 percent content of mater mass C mhich

is represented in Figures 6.25 and 6.27 by the dashed Une. The signi-

ficant increase in the contraction on mixing in the horizontal direction

(at different depths) from the subarctic structure 'AB' totheleqUatO'rial

structure CB is apparently one of the reasons why the latter

is more stable, and reflects the result of mixing not only of the mater

masses C and B themselves, but also the participation of water mass A in

the mixing .. Thus, the bulge in the equatorial T-S curve in Fig. 6.13 to

the left, in the direction of the T-S index A, may be entirely the result of

this very process.

It should be pointed out that the above type of mixing, strictly

speaking, is not horizontal, inasmuch as the isopycnic surfaces, especially

in the frontal zones, are inclined, and therefore it would be interesting

to supplement the analysià of this phenomenon of increase in density mith

an investigation of the problem of the intermixing of water of increased

density from certain levels toward others (Zubov, 1957b).

Sec. 50. Ificabil1 Iii DENSITY RESULTING FROM-THE MIXING OF FOUR 'WATER MASSES

Let us examine the problem of the increase in density resulting

from the mixing of four water masses of the ocean which are homogeneous

in temperature and salinity, and for this purpose we shall select a case

where a minimum of two (or even two pairs of) initial water masses are in

the process of horizontal or isopycnic intermixing. This type of mixing of

four water masses has already been noted above (Sec. 47) and shown in

19

Fig. 6.21; it is of especial interest because it is in just such regions

of intense horizontal exchange that subarctic and subantarctic (inter

mediate) . waters are formed, and the influence of the increase in density

on mjxing on their formation may be quite appreciable.

The selection of a region of the subarctic front which lies

directly to the southeast and east of the coasts of Japan is justified

by the fact that the increase in density on mixing in this region was

studied by V.A. Bubnov (1960); thus, we have the opportunity of comparing

data on the increase in density obtained by different processes.

In Fig. 6.28 (which in its turn wi-Js the bai s for Fig. 6.21) are

plotted three T-S curves, taken from the paper of Koizumi (1955), namely:

T - the mean annual curve for the weather ship Tan(ro

29°U, 135°E);

- the mean annual curve for the weather ship Extra (39°N,

153°E);.

Ca-119 - the curve of station 119 occupied by the ship Carnegie,

on 7 July, 1929 (450 24' N, 159° 36' E).

These three curves reflect very well the thermohàline conditions

in the region of interaction of the waters of the Kuroshio . and the

Qyashio: station T is located in the region of the core of the Kuroshio,

somewhat to the. south of it, and the T-S curve reflects aptly the structure

of this current, areeing with other averaed T-S curves for Kuroshio

region. The T-S curve of Ca-119 is characteristic of subarctic waters,

and the T-S curve of station X located in the frontal region, is

representative of waters formed as a result of the interaction of water

masses of the Kuroshio and subarctic waters. The line connecting the

0

A 08

° C 23 r

20

61 -2

15

10 / 2 r,- 25:1

21°

0 ' 32.5 33,0 33,5 34,0 34,5

I t /1< 1 //

1'1 r_t. J. L

k\' 0.57 /15

- i;• .922

20'•o t, I t t It !

35,05%0

2

20

positions of the three stations on the map intersects the entire region

in which we are interested, where these waters of different structures mix.

' In Fig. 6.28 are also plotted the thermohaline indices of the four

water masses whose increase in density on mixing we shall discuss, namely:

A (10.0°0; 32.9%. ) a surface subarctic water mass:

13 1:c. 6.2S. T. cianumi 110 ,...F.pplte.:;>::11:> (e•Cc.-119?). or-p.'suellublx • c .rainlv•i u a TaK.,-;;, -.! iterbt- . . pexyrontomu: .71[3CD CNiCtirtniiiii t(ztiti)ex outttx .‘iaCC i pailotie cy6:1p1:rutle-

cKoro Ctq:(.)irra Ti:Noro cd:catv_e. •

:31•arpa::tif.3.ulasni onao -1;")>>50 (cp. c tfC. 6.1.19).

- Fig. 6.28 1. T-S curves of CarneJde station 119 (Ca-119), averaged stations

of the weather ships Tanj) IT) and Lxtra ( K), and also Ofthe mixing quadrangle ABCD of four .ater masses in the region of the subarctic front of the ?acific Ocean.

2. Line ab is the line of the maximum increase in density on mix-ing. the hatched oval is the reeon of the maximum increase in density, UP:A() :."; -=30 (compare wit1 Fig. 6.29).

21

B(22.0° G; 34.9H- ) - water mass of the core of the Kuroshio

current;

C(7.0° C; 31^.2;o) - intermediate water mass (of subarctic

origin) characterized by a salinity minimum;

D(1.0° C; 33.1;^!) - subarctic subsurface water mass (temperature

minL-ntLm.) .

The positions of the indices were determined from the extremes 2S

of the T--,S curves in agreement with the "geometry" of the T-S curves,

except for the A index, the position of which is somewhat arbitrary. It

was found on the tan^ent to the T-S curve of station 'Ca-119', and its

tempert.ture was corrected according to Japanese climatic charts.

All four original water masses mix in the zone of the subarctic

front; as already stated, water masses A and D, like waters- B and= C, mix

vertically, waters A and B mix horizontally, and waters C and D mix together

approximately along isopycnic surfaces. In turn, the products of the

vertical mixing of waters A and D, and B and C. also mix together along

surf-aces of the same percentage composition. Thus, any T-S index which

lies within the c$uadran^Yle of mixinr ABCD can be rebarded as the result

of mixing of four original water masses in different proportions..

Values of the de:nsity increzzse resulting from the mixing of those

four t•rater masses within the mdxing a,uadrE.ngle were computed by the method

proposed for constructing the mixing triangles (Sec. 48).. The grid depicted

in Fic,..6.20 was used in this case. Values of the potential density d,

(or the potenti.-,l specific volume -v;, ) were tG<tien from the T-S dia;r;sm for

each of the 121 "rid points; the average density, or the "density of mixing,"

& kag corlputed from its linear change along the straight lines- of the grid -

with allowance for the fact that the potential densities at the apexes A,

22

B, C and. D are equal to the true values, ncmely, 2503, 24.14., 26.80 and

26.54 respectively. This abbreviated method of computing average density

is equivalent to computinü it by the mixing formula for density,

where ••6, mD

nz AGA -!- ntR17 N n:r°c 4 - n'n`D

, nzA =, rnB ; rttC -T- mn(50.1)

are the percentages of each of the four water masses

at any point 11 which can be determined from the percenta^e nomogram

illustratil,d in Fig. 6.21.

The picture of the density increase resulting from the mixing of

four water masses is shown in Fig. 6.29 in the form of isolines of smoothed

values of the density increase,105 102 & Cr =102 r0-7- (S-T)

tŸll2Sy we have a qt^,l(^ 1TF,?1:;1e of densit ^ncrcase- Can PlixJ_nn. This quadrangle

shows that the increase in t.rater. density on rnixino, 105, , varies in the

region of the Pacific subarctic front approximately between 5 and 30

(10-5 ü.cm-3) and the maximum value is 33. The line ab of maximum density

increase extends from the structure LD (surface subarctic waters) to the

structure BC (Kuroshio waters within the troposphere), while the region of

maximwn density increase, 105d (_);^30, is shifted toward the Kuroshio

structure. In analysing the increase in dens3ty i^esulting, from horizontal

mixing of subarctic winter waters and Kuroshio waters by the method of N.N;;

Gubov, and K.D. Sabinin, V.A. Bubnov obtained the sar.ie value, 1051.1P .-

32; lie investiÜated the mixing of two waters alon" a mixing line close to

the straight line T'D, t•:hich, as can be seen from Fig. 6.28,• also crosses

the re:^icn of maximum densit^r increase on the T-3 diagram (hatched

area in the figLtre) .

* See translator's note on page 4

23

20

- 15

5

0 32,5 33.0 33.5 34.0 34,5 35,05 '36.

D • 1

T °C

?sr

1. Pt:c. 6,29. 1-1c7:;1'perirc.v,littb: yiLiontelt;iri r;Du . • mace A. 8, C i D.

•

Fig. 6.29 1. Quadrangle of density increase resulting from mixing (10 5Ly

of water masses A, B, C and D. 2. Line ab is the line of maximum increase in density.

Let us now compare very generally the conditions under Which the

water density increasoson mixing with the thermohaline conditions 5n the

Tegion in question. To this end, let us turn again to Fig. 6.28 which

also shows the line ab of maximum increase in density and the region of

maximum increase in density, (hatched oval). Inc line •

of maximum increase in density lies approximately between the isopycnics

== 25.8 and 26.0; consequently, the re L;ion of the maximum increase

in density in the ocean lies in this isol):!nic layer. This layer gradually

• 2 =1 . ...WIWI —.11:111SR Ita;(60.1bill2r0 YTMOtHentIll. . •

288

24.

slopes between statiens X and T, i.e. in the region of the most intense

interaction between the Kuroshio and the subarctic waters, from the north-

east to the southwest from a depth of 50-75 m to approximately a depth of

400M (segment cb of the line ab in Fig. 6.28); this can be seen from the

distribution of depths along the T-S curves.

The line DC represents the line of transformation of interme-

diate cold waters, D, in the intermediate layer with a salinity minimum

C; this transformation occurs approximately along the isopycnic surface

C26.75, as was noted earlier by Hirano (1957). The density increase

••••••••■••••■•■■•••••■■••

AD 3 % (Boas, OÛRCUO) • (8oeu leypocuo)

SO rz,-..

60 [

i

i----T-A------/11 10 5.A ID 10 =

a 33

eP rtec -150 1 I 1 5 •C 1

(Or 5N. D ':

I ' 201- _ c. - - ...1

1 I Y*".■-_.- 101- _."-_---<- 1 i

1 I 1 - 1 I I I

. • • .. . ,. • .. • • -: . . • • . ..1 * Pue; G130. l(purme npoueuruoro collsep.;;:auun Bo.aubtx.

' itacc A, B, C u D BÂO.lie .11:11111I os maKcilmaibuoro yuaor- .

liC/1119 111:11 CMCII.t...fillit. • . :: , 2 Ed:bimfiti..! yir.loritesnqnor:a3alc,r_ urrpitxoson Kplitiori,

AD — BO1 0:1qC10, BC — 60U.1 iïifocito.

3 -

Fig. 6.30 1. Curves of the percentage of utter masses A, B e C and D along

the line ab of maximum increase in density on mixing..

2. Values of the increase in density are shown by.the dashed curve.

3. Oyashio waters 4. Kuroshio waters 5. Maximum

AD 3 ec 4

30.

20

10. . .•

on mixing along the line DC is the least in the entire region; however,

the transformed waters also slope from the northeast on to the southwest

(from station 'Ca-119 to station ST 1 ), from a depth of 50-100 m to

approximately a depth of 500-800 m (Fig. 6.28). Without going into details,

we can assume that this sloping produces some increase in density in the

overlying layers.

A quantitative estimate of the influence of an increase in

density on the mass balance of the ocean cannot be obtained without

analyzing the content of each of the original waters in their mixture;.

some ideas regarding this can be derived from a comparison of the quadrangle

of the density increase with the percentage nomogram ("Fig. .

Let us examine as an example the change in the percentage of each

of the water masses along the line of maximum density increase on mixing,

ab, which is also plotted on the percentage nomogram. The curves of the

percentai,:e of each of the waters are also plotted separately in Fig. 6.30

(also plotted here is the curve of the density increase on mixing along

the . line ab - the dashed line). It can be seen, in particular, that the

maximum increase in density, equal to 105Ap=33, occurs on mixing of one

third of subarctic waters with two thirds of Kuroshio watersI this ex-

-plains the proximit3r of the zone of the maximum density increase to the

Kuroshio region, compared with the subarctic region. A more detailed

picture can be obtained from an analysis of a sufficient number of T-S

curves from stations located between station Ca-119 and the weather ship .

yang°.

It is well known (Sec. 30), that in a case where the mixing of

three water masses is being investigated, the increases in density on

26

mixing are given by the difference between the density deter:nined by the

true equation of state of sea water CTr = (TT -T), and the density

corresponding to some linear equation of state.. The latter is explicitly

deterniined by the density values at the apexes of the mixing triangle,

given by the true equation of state; the true and fPavera^e'i densities

agree at these three points (apexes) of the triangle. ;v"nen ttio, four, or

more water masses are mixed, we have a dif.^_e-rent picture. "'Rien two water

masses mix, the equation of state, correspondinp to the distribution of the

"average" density, i.e. equation is linear along the

mixing line of these two water masses; beyond this se,^gment it can also be

nonlinear, generally speaking. Thus, we can prescribe any linear equation

of state corr.esoondin; to the linear distribution of density along a given

mixing line; these equations will be determined explicitly by the con-

stant (arbitrary) values of the coefficients of thermal expansion _cx..and

the "contraction" salinity ,Q in the expression for the linear equation:

aT -2S

(.c7a is some constant value of the potential density).

If we analyze the density increase resultin.-1- from the mixing of

four wr.ter masses, the true and l'a.vera-e" densities agree at the apexes

of the quadrangle, and the density distribution is linear alon.f the sides

of the quadran;le, and also along the lines of the Erid illustrated in Fig.

6.20. Iiowever, within the mixinu quadrailvle^ the equation of state will

be nonlinear, except for one particular case, which we shall discuss

below.

37 The possible Ceneral.ized formal concept of "e;.p^zns ion on r.iixin:;u out-side of a mixing triangle or qùadran^^e is not considered liere;

7 ° C ,

lU 64• e •

i ' • 8

27

Let us illustrate the foregoing by the following example. Let 290

un assume that the isopycnals on the T-S diagram represent the topographic

contour lines of the function er (S-T). In this case, the true equation

of state will be represented in the form of a smooth curvilinear surface,

rising into the region of high salinities and low temperatures and having

a smooth inflection along the temperature line of maximum density. The

plane corresponding to the linear equation of state contains three points

that correspond to topographic elevations of the surface of the true

equation of state at the apexes of the mixing triangle, and intersects

1 . Pile. 6.31. TKyro.-r,..tinKti yrutott-mtori (10' 3p) npit pai.e..n.dtom ote : HICIIIIII F.o,:olux mace À, B H C u i1 C ii D COOTHeiCTBIIIII10.

îptoie.

• :Mum nkiniu It?.Kciimardatipro yn:1071ICNH1. ••• • • •

• Fig. 6.31 1., Triangles of the increase in density (10 5.àp), resulting from

the separate mixing of water masses A, B and C, and A, C and D respectively. 2. The dashed lines are the lines of maximum increase in density.

28

with the latter On some curves connecting these points. Finally, the

surface constructed from the true density values at the points of the

mixing quadrangle is a second-order curvilinear surface and corresponds

to the' nonlinear equation of state for the average density

determined by formula (50.1). This equation can be linear in one particular

case, i.e., when the four points (apexes) of the mixing qnàdrahgle) lie

in the same plane. This curvilinear surface "sags" with respect to the

surface of the true equation of state, and the families of straight lines

(grid in Figs. 6..20 and 6.29) are its generating lines (within the

quadrangle),

Fig.. 6.31 show (for comparison with Fig. 6.29) triangles of the

density increase on mixing ABC and ACD constructed on the assumption

that the wrater masses D and B respectively do not participate in the mixing

of the other three water masses. We can see that the general pattern

within the two triangles differs from the pattern of the density increase

in the quadrangle, observed during the mixing of all four water masses.

These differences are quite substantial although the general pattern of

the density increase is approximately similar (the region of the maximum

density increase is shifted toward the straight line of mixiru BC - Kuroshio

structure),

A comparison of Figs.. 6.27 and 6.31 to some degree supports the

hypothesis of "horizontal" mixing of water masses along the surfacea:cif

equal percentage content, which served as the basis for the construction

of the mixing quadrangle, (Sec. 47); within the region of interaction of

the waters there is no line of zero density increase on mixing,(i.e. the

line AC in Fig. 6.31), the nature of the increase in density resulting

291

from the vertical mixing of waters A and D and of the waters B and 0 is

the same in both cases, but at the same time there emerges a region of

maximum increase in density within the region of interaction of the four

water masses.

Sec. 51. STAT1STICUL T-S ALYSIS

The object of statistical T-S analysis is to determine the

reproducibility of observations corresponding to given points on a T-S

diagram or to certain squares on it. The study of the reproducibility

of T-S relationships, which can be classified according to Ltemperature

and salinity, can be carried out on the basis of time, space and volume.

Statistical T-S analysis broadens considerably the possibilities of T-S

a•alysis on the whole; as we have already-seen. the latter' was applied

previously, principally to individual T-S curves.

Statistical T-S analysis was proposed bY Montgomery (1955), and

we shall consider primarily his work. Observations numbering 540, which

were made on the temperatUre and salinity of the surface of the sea in

the course of the years 1943, 1949 and 1950 from the weather ship J in

the 1;orth Atlantic (mean position: cp 53 • were used by

Montgomery to construct

29