Deep-Sea Research, Vol 34, No 4. pp 531-546. I98?Printed in Great Britain

0198-0149/87 $3.00 + 0 00

@ 1987 Pergamon Press Ltd.

The relationship between ocean current transports and electric potentialdifferences across the Tasman Sea, measured using an ocean cable

PBren G. BerNes* and RossRr C. BBr-r-*

(Received 4 March 1986; in revised form 29 September 1986; accepted 30 September 1986)

Abstract-An attempt is made to interpret observations of electrical potential differences acrossthe Tasman Sea in terms of ocean currents. This voltage record (spanning 7r1 years) is significantlycorrelated with the (monthly averaged) mean sea level at Sydney, but not with that at otherlocations. A numerical model of the Robinson type for the Tasman Sea region permits thedetermination of the cable voltage which results from a given oceanic current pattern. Most of theobserved voltage variance is probably due to East Australian Current eddies close to Sydney.

I N T R O D U C T I O N

THB measurement of electrical potential differences in seawater across substantialdistances by means of submarine cables and the attempted use of such measurements toinfer the water transport across the intervening region have a long history, going back toFaraday. The basic notion is that as seawater moves horizontally through the earth'smagnetic field, it generates a potential difference between the two sides of this fluidcurrent which is proportional to the fluid transport; the latter may then be inferred frommeasurement of this potential difference. In practice this situation is complicated by anumber of factors, such as time dependence, complex geometry, and the partial short-circuiting of the generated voltage by non-moving conductors such as sediments,stationary fluid, and even the earth's crust and mantle.

An additional and more serious complication is the fact that variations in the earth'smagnetic field will induce currents in the cable and hence produce a signal regardless ofocean current effects. The situation for long ocean cables (the subject of this paper) hasrecently been summarized by Mslont et al. (1983). Such magnetic variations may be dueto solar-related fluctuations in the magnetosphere, high above the earth, or to telluriccurrents caused by motions in the earth's core and the geomagnetic dynamo. Anadditional unknown factor is due to the possible chemical potentials at the electrodes;changes of this nature will probably occur slowly, and will be ignored here.

In spite of these difficulties, a direct relationship between ocean currents and cable-measured electric currents has been established for a number of locations over moderatedistances, most notably perhaps, the Straits of Dover and the Straits of Florida. Themodel used to relate the voltages to the ocean currents range from the simple expressionderived by LoNcunr-Htccms (1949) to the elaborate numerical models of RosrNsoN(1976, 1977).

* CSIRO Division of Atmospheric Research, Aspendale, Australia.

531

532 P. G. BAINES and R. C. BELL

In most locations the most prominent component of the voltage signal is tidal. Sincethe ocean tides are reasonably well-known in many locations, the cable signals may becalibrated, but such calibration is not generally valid for low-frequency motions (Ronrx-soN, 1977). Recent observations of the Florida Current by SeNrono (1982) and Lansr,Nand SeNpono (1985) give encouragement that for cables of moderate length the methodhas practical value for the measurement of low-frequency currents. The interpretation ofvoltages measured with long ocean cables is more difficult. Whereas simple models maybe adequate to describe the relationship between ocean currents and cable voltages overmoderate distances such as straits and channels, more elaborate models are necessary forcomplex flow patterns in large regions. However, the possibilities of obtaining somedirect measure of the components of the circulation of ocean basins are tantalizing, andthe effort seems well worth-while. To this end, it is necessary to understand the factorscontributing to the observed voltage signals as well as possible.

The object of the work described in this paper is to attempt to interpret the observedlow-frequency voltage data-obtained using a cable running across the Tasman Sea fromAuckland to Sydney-in terms of ocean current transports, and to place limits on thepossible contribution of the latter to this voltage signal. To achieve this, we haveconstructed a numerical model of the Tasman Sea region of the Robinson type, whichenables the calculation of cable voltages from known ocean current patterns.

O C E A N C U R R E N T P A T T E R N S I N T H E T A S M A N S E A

Current patterns in the Tasman Sea show substantial variability and, like the circula-tions in most ocean basins, are not well understood. The strongest currents are found inthe deep region to the west of Lord Howe Rise (Fig. 1) where the southward-flowing

East Long i tude

Fig. 1. Topography of the Tasman Sea. Depths are given in thousands of metres.

o

($

b 0

2g"s

32"

34 "

360

1 l th December 198O

152"E 154 1 5 6 "

1 5 2 " I 5 4 0 1 5 6 0 1 5 g o

1 5 g o 1 6 0 "

1 60"

2gos

3 0 0

{g2"

34"

3 6 0

I 500E

Fig. 2. An infrared satellite photograph from NOAA-6 showing a typical East AustralianCrirrent configuration off Sydney. Lighier colour implies colder,water..Note eddy "Maria"

forming by ;pinching off"- Provided by R. Legeckis (NESDIA, U.S.A.) and G. Cresswell.

Ocean current transports across the Tasman Sea 53s

East Australian Current (EAC) occurs. This current flows southward along the Austra-lian coast with a typical transport of 30 x L06 m3 s-l (i.e. 30 Sv) until ii reaches thelatitude of 32oS, where it separates from the coast in the vicinity of Sugarloaf Point [seeGoornBv et al (1980), BoI-aNn and CuuncH (1981) and references contained therein].The current is generally larger in summer than in winter by up to 50%. The separatedcurrent normally turns northeastward and meanders and becomes more diffuse (Fig. 2).Warm anticyclonic eddies may become "pinched off" at the southern bend in the currentin the neighbourhood of Sydney at a rate of 2 or 3 per year. Such detached eddiessubsequently have an unpredictable behaviour and may have a lifetime of a year or more.Many of them ultimately become reabsorbed into the EAC system; escape southwardtoward the southern ocean is rare.

The other conspicuous feature of the Tasman Sea circulation is the mid-Tasman frontbetween 30'S and 34oS, extending from near the Australian coast to the North Cape ofthe North Island of New Zealand with a typical transport of 15 x 106 m3 s-1. This frontmay be seen as an extension of the EAC system, but it is highly variable with largemeanders (Annnews et al. , 7980) and at times may be very weak (Cor-evraN , 1984) . Apartfrom isolated eddies, currents elsewhere in the Tasman Sea appear to be generally weak.To our knowledge, no estimate of the net transport through the Tasman Sea from thenorth to south has yet been given.

T H E V O L T A G E A N D M E A N S E A - L E V E L D A T A

The data were provided to the authors in the form of an unpublished manuscript byRuncorn, Richards, Strens and Molyneux, here after denoted RRSM. The setting up ofthe observations was described by RuNconN (1964). Although there are extensive data (7years or more) for three long cables (Sydney-Auckland, Auckland-Suva, Suva-FanningIsland), we decided to concentrate on the Sydney-Auckland cable and the Tasman Searegion.

Details of the data collection and processing are described in RRSM. The voltage data,in the form of 29-day means, are shown in Fig. 3, and cover the period from March 1969to September 1976. The choice of this period has the effect of removing virtually all ofthe effects of the diurnal and semidiurnal tides from the record. This interesting recordshows large fluctuations of the order of +0.5 V, with periods of several months. We aimto determine how much of this record may be attributed to ocean currents.

0 60 40 2

o 0z n . )

0 40 60 8

1969 19'.10 1971 1972 191) 19'14 1975 1976

Fig. 3. Auckland minus Sydney monthly mean voltages (from RRSM-see text),

536 P. G. BaINes and R. C. Brll

Sydney

1969 1970 1971 1972 1973 1971 1975 1976

Fig. 4. Monthly mean sea levels at Sydney corrected for atmospheric pressure,

The voltage record has been compared with other records for the same period, whichrelate to the ocean currents of the region. These are the monthly mean sea level (MSL)records at Sydney (Fig. 4), Auckland, Lord Howe Island and Norfolk Island. TheAuckland record is from March 1969 to December 1973 only, and is on the Pacificside. These MSL records have been corrected for atmospheric pressure, in that the localisostatic response to variations in atmospheric pressure has been removed, and theyprovide a crude measure of the ocean current activity via the geostrophic relationship.Part of this MSL variation will be due to "steric" changes, which are changes in MSL dueto variations in the temperature and salinity of the nearby deep water column. Suchchanges in MSL are mostly isostatic (Parruu-o et al., 1955; Grll and NnLen, 1973),meaning that they do not affect the bottom pressure and hence are not relatedgeostrophically to barotropic ocean currents. CHURcH (1980) found that 44"/" of the totalvariance at Sydney could be described by a linear regression equation, giving acorrelation coefficient of 0.75, so that this proportion of the Sydney MSL variance can betaken as isostatic. However, the length of the joint record and the nature of the data donot justify making a correction for this effect here.

There is no significant correlation between the Auckland and Sydney MSL records, orbetween the Auckland, Lord Howe Island, Norfolk Island MSL records and the cablevoltage record, but the Sydney MSL record and the cable record have a correlationcoefficient of 0.33, which is significant atthe99o/o confidence level (if each29-day point isassumed to be independent). This suggests that a substantial part of the variation in thecable record is directly related to ocean current patterns in the western part of theTasman Sea. On the other hand, currents in the eastern part appear to have little effecton the cable voltage. This is consistent with the known ocean current patterns in theTasman Sea, as described in the previous section.

T H E O R E T I C A L B A C K G R O U N D

The equations for the voltage induced by a time-varying flow are considerably morecomplex than for a steady flow. However, if the flow varies on a sufficiently long timescale, local steady-state may be assumed. For flow varying with frequency co, thecondition for this to be valid is (SnNnono,l97I; RoarNsoN, 1976)

o F. 0. L d <'J. , (1 )

l 3

1 2

;o

+ t lo

Ocean current transports across the Tasman Sea 537

where L and d are horizontal and vertical scales, p, is the magnetic permeability ofseawater and o, its electrical conductivity. For this Tasman Sea situation whereL : 2270 km, d - 4 km, this parameter :0.07 for 29-day periods, but -4 for I2-hperiods. Hence the steady-state assumption is valid for 29-day averages, but not for tidalfrequencies.

If fluid flows with uniform velocity v along a uniform channel with semi-elliptical crosssection, the voltage difference AQ between the two sides of the channel is given by(LoNcuer-Hrccns, 1949)

A 0 :vBrL

volt,1 * o6 Ll(2a-d)

(2)

where B, is the vertical component of the earth's magnetic field (in teslas : 70-4 G), Land d are the respective width and maximum length of Jhe channel (in metres), and o-and o6 are, respectively, the conductivities (in mho m-') of the seawater and the semi-infinite medium below the channel. The medium above the channel (air) is assumed tohave zero conductivity. In most oceanic situations we have dlL < 1; given this, Longuet-Higgins further showed that equation (2) is good when the fluid velocity varies in thevertical, provided that v is interpreted as a vertical average of the horizontal velocity.

In practice, particularly when long horizontal distances are involved, v will varysubstantially in the horizontal, the geometry cannot be well-described as a uniformchannel, and the conductivity in the surrounding medium is not uniform. Consequently,more sophisticated models are required. Such models have been developed by RonnsoN(1976,1977) and we follow his procedures here.

Robinson's model is based on the result that, in steady-state, the observed voltagedifference A$ between the two electrodes may be expressed as

AO -- |"w . v dv, (3)

where the integral is over the whole volume of the fluid, v is the vector fluid velocity, andW is a vector which depends only on the geometry of the system, the conductivity of theseawater and surrounding medium, and the magnetic field. This result, established byBsvtn (1970), may be obtained from the steady-state equations of magnetohydro-dynamics, namely

j = - o V O + o v X B ,

v ' j = o ' ( 4 )

where j is the electric current density. In the present context we consider a situationwhere a unit of current is passed from one electrode (1) to the other (2) with the fluid atrest, and denote the corresponding current density and voltage byj" and $u, respectively.These quantities will satisfy the equations

j , : - o V 0 , , V . j , : 0 , ( 5 )

outside the electrodes. Ifj and $ denote the current density and potential caused by thefluid motion and hence they satisfy (4), we may write

J' V ' (0j, - 0;) dv : .[s,*s, (0j" - 0,j) ' ds, (6)

538 P. G. BATNEs and R. C. Brrr

where V denotes all space excluding the electrodes, and 51, 52 denote the surfaces of theelectrodes. We also have

J s , i ' a s : 0 : J s , i ' d s ,-[s, i, ' 65 : -Js, j, ' dS : L'

from equations (5) and (6). Then, since in each situation the potential is constant on eachof the (relatively small) electrodes, we have

0, _0, : - [u 0, . vo_j . v0,) dy: - J v o V 0 " . v x B d V

( 8 )

which is equation (3) with W : B x i,.Hence the cable circuit observes a spatially and directionally weighted average of the

whole velocity field, with the strongest weighting in the region of ocean in the vicinity ofthe cable. This expression for the voltage as an integral gives the model a certainrobustness as a measure of total transport.

T H E N U M E R I C A L M O D E L

If W is known, the voltage induced by a given velocity field may be calculated fromequation (3). The first problem is to determine W : -oB x V0, by solving for Su, with aunit current passed between the electrodes and ignoring the cable.

In the Tasman Sea region (Fig. 1) the model employed 1'Cartesian grid resolutionwhose boundaries were placed at26oS,49"S, 141"8 and 184"E: 176'W (Fig. 6). Thisgives a 45 by 25 grid, including points outside the boundary. The conductivity structurebeneath the Tasman Sea region is poorly known and is probably rather complicated dueto the presence of submerged continental features such as the Lord Howe Rise and along-defunct spreading zone, the Dampier Ridge (vaN nen LINDEN, 1969). For want ofsomething better we assumed that the conductivity was horizontally uniform, and for thevertical structure we used an approximation to the profile obtained by Fn-loux (7977) torthe northwest Pacific (Fig. 6a). A simplified version was chosen as a basis for the mode-(Fig. 6b). The variable depth of the ocean and the disparate thickness of the layers ofconstant conductivity create difficulties for numerical computation. These have beencircumvented for the calculation of $,, by assuming a top layer of uniform thickness.of7.7 km incorporating seawater, sediment and part of the crust, with a spatially varyingconductivity which is a vertical mean over this distance (using the profile in Fig. 6b). Thisapproximation is justifiable because the horizontal length scales are much larger than7 .7 km; consequently the resistance to electrical currents in the vertical in this compositelayer is much smaller than that to horizontal currents, and the layers behave likeconductors in parallel. In other words, the variation in voltage $, through the depth ofthis composite layer is small. The conductivity of this layer is given by

(7)

1ot =

4 (o* d** o" d" + o, dr), (e)

where the subscripts w, .s and c refer to seawater, sediment and crust, respectively, with

Ocean current transports across the Tasman Sea 539

Dr : d* + d, + d, : 7.7 km. The model containsnesses and conductivities are shown in Fis. 6c. With

three lower layers, and their thick-this grid the equation

60 km

I

V' (oV$") : p (10)

is then solved, with oV$" : 0 on the boundaries and p zero everywhere except at thesource and sink points at the locations of the ends of the cable, where p : +IlLxLyL,z.

The solution for $, was obtained by the following procedure. Firstly, an initial guessfor $ was found from an inverse square distribution about the source and sink. From this,the approximate electric current field from the topmost to the second layer was found.Using this field as a forcing term, an exact solution for S in the upper layer was obtainedby the method of LrNrzeN and Kuo (1969), and an approximate solution for $ in theother layers was found by successive line over relaxation (SLOR-see for example Aues,

Fig. 5. Topography of the Tasman Sea region.as used in the model, showing depth contours inmetres.

o lS n-r l

lo-t to-2 ro-t loo

o = 3 3 T77 km

200300400

- 500E5 600f 700

o = 0 0 0 2 87 km

o = 0002 5 1 3 k m

O = U U T

( a ) t b )

Fig. 6. (a) Electrical conductivity profile proposed by Frlloux (1977), based on magneto-telluric data from the northeast Pacific. (b) An approximation to the electrical conductivityproposed by FILLoux (1977) shown in Fig. 7a. (c) The layers used in the model, approximating

those of Fie. 7b.

( c )

b \ o

o = 0 002 60 km Crust

( o )

540 P. G. BnrNrs and R. C. Bell

Fig.7. (a) The virtual current field j,, in the seawater obtained by passing one unit of currentfrom Sydney to Auckland. (b) The weighting function W = B x i,. (c) Wd, the W field

integrated over the depth d of the ocean.

( b )l l

t lt lt l

. t t t l

. . . r . l l l

l l l l r r , . ,

l l t t ,

t r t , t

t a r t t t . .

t , l r t . . . .

t r a u a

. . a a -

f ' t . , . , . . ' "t \

l . i r l lr , l l l ll t l r l l

t . I l t r

t r , t . .

: n ! t t

l t r t lI t f l rI t t t It I t t Ir I l t r

;

I

IIt

:

{tI

I

t

{1I

1I

t l

, ,

Ocean current transports across the Tasman Sea

1969). A new vertical electric current field was computed from this new $, and the wholesolution process was repeated until convergence of the solution was obtained. About 30iterations were required for 4-figure accuracy. We then have j, : -6* V Q" in the ocean;and W : B x ju, where the earth's magnetic field was obtained from BaRRacloucH andMarIN (1971). The cable voltage for a given velocity field is then given by equation (3),where the integral is taken over the whole body of seawater, using the depths shown inFig. 5. The vector fields j,, and W are shown in Figs Taand b, respectively. Note that theseare strongest in the vicinities of Sydney and Auckland, and hence that the cable signalshould be most sensitive to current fluctuations in these regions.

Figure 7c shows the integral of W with respect to depth. Here the significance of the"Auckland end" is substantially reduced because of the shallow depths in the easternportion of the Tasman Sea. Consequently much larger barotropic velocities than in theSydney region are required there in order to have the same magnitude of effect on thecable voltage.

I N F E R E N C E S F R O M T H E N U M E R I C A L M O D E L

The model described above has been used to calculate the cable voltage produced by anumber of ocean current patterns in the region. Since only barotropic currents affect thecable signal, these current patterns will be specified as vertically integrated transports.We can define coordinates x (eastward) and y (northward) where x1(y) denotes theAustralian coastline or the left-hand boundary of the model, and x2$t) the New Zealandcoastline or the right-hand boundary of the model. For uniform north-south flow wherethe transport is independent of x, the model gives an overall transport of 197 Sv V-1,southwards for positive voltage (Auckland relative to Sydney). The mean cable voltageover the period of observation is -0.17 V, which would correspond to 34 Sv, northward.This figure is comparable with the observed southward transport of 30 Sv in the EastAustralian Current, and would imply a uniform velocity of -0.4 cm s-l. The direction ofthis net transport (northward) is consistent with the "classical" belief manifested in theatlas of Schott of 1942 (DenaNr, 1961; NeurraeNN and PrERSor.r, 1966, p.424), althoughthere has not been any suggestion of a northward transport of this magnitude throughthe Tasman Sea from conventional oceanographic observations and it is probably muchtoo large, as discussed below.

The figure of 197 Sv V-r for uniform flow may be compared with the correspondingresult from the Longuet-Higgins formula (equation 2). Taking o-: 3.3, oa : 0.02(ohm m)-1, B,: 5 x 10-s teslas and a mean depth of 4 km, equation (2) gives191 Sv V-r, which is consistent with the cable result. However, this agreement may bepartly fortuitous for the following reasons. Firstly, the model assumes (effectively) zeroconductivity at depths below 127.7 km; in practice, electric currents are expected topenetrate down to depth of order L (2270km), so that the model would overestimateA$. Estimates based on simple circuit theory show that this error should be small becauseof the inhibiting effect of the low-conductivity crust layer. Secondly, W does not vanish atthe lateral boundaries of the model, implying an overestimate for A$ due to thehorizontal truncation. The agreement with equation (2) may be partly attributable to themutual cancellation of these two effects. Taken jointly, these considerations are notregarded as serious deficiencies. The numerical model may therefore be used with someconfidence to investigate the effect of non-uniform current patterns on cable voltages,taking into account the variable bottom relief and the conductivity profile.

541

< n 1 Berurs and R. C. Brr-l

It is possible for the cable to register voltages with no net north-south transport at all.To take a simple example we define a line x3$) by

xz!) : x{J) + c{x2(y)-xr j ))

and a north-south velocity v by

(1 1)

d .v : c2 l (40) -x t (y ) ) , * <x t (y ) ,

: c2l(4$t)-xzj)) , x> xt(y).

with east-west velocity u : 0, where c1, c2?ta constants. The flow is oppositely directedon each side of .r3Q), with zero total north-south transport (shown schematically inFig. 8a). If c2 is chosen to give a transport of 50 Sv on each side of x3, with v positive forx I x3, the cable voltages obtained from the model are shown in Table 1. These resultsshow that a narrow, strong stream is less effective in generating a cable voltage than abroad weak one with the same transport. This is because the voltage generated over ashort distance is more easily short-circuited through the deep underlying medium thanthe voltage generated over a larger distance. Hence, cable voltages may be produced byeast-west asymmetry in the north-south current, and the larger the asymmetry the largerthe voltage. If the moving fluid is assumed to have a northward velocity which is uniformwith longitude (x) (rather than uniform transport), the cable voltage for 33.5 Sv is

x ' (y ) xly) x1(y) xlv )

Fig. 8. Schematic representation of Tasman Sea ocean current patterns studied in the model.x1$) and.r2(y) denote the western and eastern ocean boundaries of the model. (a) Uniformnorth-south transport; (b) large eddy pattern (m = I, n : 2); (c) East Australian Current and

mid-Tasman front; (d) eddy near Australian coast.

Table 1.. Cable voltages obtained from the model with the flow pattern given by equation (12)

(12)

x3(y)xr(y) xr(y) xly)

( b )

c1 0 .1Voltage -0.124

0.2-0.072

0 .4-0.027

0.50.011

0.90.113

0.6 0.80.009 0.057

Ocean current transports across the Tasman Sea

-0.15 V, slightly less than the uniform transport figure of 4.I7 V, and this may beattributed to the effect of non-uniformity in transport due to the variations in depth.

The effect of large-scale flow patterns may be demonstrated by taking a transportstream function (du : -}yldy, dv : dy/Ox)

xz9) - x{y)srn c4y,

where m is an integer and the origin for y is at the southern boundary of the model(49'S). We take cq: tt. 3.533 x 10*7 m-l with n an integer to give integral half-wavelengths, and choose cr : 50 x 106 m3 s-1. This represents a doubly periodic cellu-lar flow pattern with a transport of 50 Sv in each cell (Fig. 8b). Although the transports inthese eddy patterns are large, the voltages are generally small (<0.1 V) (Table 2). Hencelarge-scale flow patterns with zero net north-south transport only have a small effect onthe cable voltage, even at large amplitude.

Another flow pattern examined was that of a 200 km wide (2 grid points) EastAustralian Current with a transport of 30 Sv adjacent to the coast. This current flowedsouthward to the latitude of Sydney, where it turned due eastward to the North Cape ofNew Zealand, representing the mid-Tasman front (Fig. 8c). This flow pattern resulted ina very small cable voltage of +0.019 V.

Finally, we considered the case of an eddy near the Australian coast. We assumed aneddy structure which consisted of rigid rotation within a circle of radius a, with potentialflow outside. The azimuthal velocity for an isolated eddy is then

where r is the radial distance from the centre of the eddy and o is the angular velocity. Ifwe approximate the nearby coastline by a straight rigid vertical boundary, we may satisfythe condition of zero normal flow there by introducing an image vortex. If the vortex iscentred at (x,, y,) (at a distance greater than a from the coastline) and the image vortex isat (x1, y), the transport stream function is given by

\ r : f ( @ - * , ) ' + 0 - y , ) 2 - a 2 ) - a 2 i . l l n ( ( ( x - * , ) ' * ( y - y , ) ' ) I t o ) , 0 < r 1 e ,

(x - x")2 +

V : , . r i n (

# ) , r l '

(13))t /

mn(x - x{y)

v : r u o ) 0 < r < a J: a 2 a l r , r > a ) '

( i4)

(1s)( r - * ) ' + ( y - y ) ' / '

With a radius a : 100 km and an angular velocity or chosen so that the transport around

Table 2. Cable voltages obtained from the model with the flowpattern given by equation (13)

X 11246

0.0120.0190.025

-0.006

-0 153-0.1930.0740.059

-0.038-0.0270.103

-0.015

544 P. G. Berres and R. C. Bpll

Table 3. Voltages obtained from the model for an eddydescribed by equation (15) with a circular transport o/ 30 Svwithin a radius of 100 km. The eddy centre is located at grid

point ( i , j ) ; Sydney is at (12,17)

,\ 15I413

7918t7t615

0.840.44

-0.37

-0.0130.22

-0.41,0.200.023

-0.0140.014

-0.29-0.019-0.073

An eddy location over land.

the eddy for r ( a is 30 Sv, the cable voltages for a variety of eddy locations are given inTable 3. These are substantial if the eddy is close to Sydney, and may have either sign,depending on the position of the eddy. Although the resolution of the numerical model istoo coarse for eddies of this size to be resolved with great accuracy, Table 3 indicates thatthe voltage variations of the magnitude of those observed, and of either sign, may becaused by eddies of realistic size and circulation when they are sufficiently close toSydney.

We also note that the effects of more complex flow patterns may be obtained by super-position of the above patterns, because the relationship between cable voltage and fluidtransport is linear.

S U M M A R Y A N D D I S C U S S I O N

The results from the previous section show that the low-frequeny cable voltagevariations may be affected by ocean currents in several ways: (i) by a net north-southtransport through the Tasman Sea at a rate of 197 Sv V-1; (ii) by an asymmetricdistribution of the north-south flow with no net transport, and (iii) by significant motionsuch as eddies near the locations of the electrodes. A simple interpretation of the meanvoltage of -0.17 V (Auckland relative to Sydney) implies a net northward transport of34 Sv, which could be achieved by a mean velocity of about 0.4 cm s-1. However, apartfrom a very narrow channel (near Cato Island), the Tasman Sea is closed at its northernend below a depth of approximately 1000 m by a broad ridge (the Lord Howe Rise).Hydrographic data, e.g. the "Eltanin section" at 28'S (plates I and II of Srovvrl e/ a/.,1973), indicate that the deeper water does not flow over this ridge, so that any significantnorth-south transport must occur in the upper 1000 m. This is the depth range of theEast Australian Current and the mid-Tasman front, which together present a barrier tonorthward flow in the western and central part of the upper Tasman Sea. This impliesthat any northward transport must occur in the eastern part towards New Zealand, butlarge and persistent northward velocities have not been reported here. Further, evidencefrom drifting buoys in the Tasman Sea, drogued at various depths down to 200 m, showno evidence of systematic northward motion (G. Cnesswell, private communication).Finally, theoretical models based on Sverdrup transport with realistic wind stress alsoshow no substantial northward transport in the Tasman Sea (S. GoorREy, privatecommunication). One is forced to conclude that the net north-south transport in theTasman Sea must be substantially <34 Sv, and that the mean cable voltase must have

Ocean current transports across the Tasman Sea

some other cause. There appear to be three possibilities. Firstly, the unknown effects ofchemical potentials at the electrodes may well produce effects of order 0.1 V; secondly,the eddies near Sydney may produce a rectified effect of this magnitude, and thirdly, itmay be due to leakage of electric currents from the earth's core, as hypothesized byRunconN (1964).

The effects of a variety of different flow fields on the cable voltage have beeninvestigated with the numerical model, but the only realistic flows which were found to becapable of producing the large voltage fluctuations observed were eddies and associatedcurrents near Sydney. Similar effects near Auckland are unlikely because strong currentswould be necessary there because of the shallower depth, and these have not beenobserved. Furthermore, the cable voltage fluctuations are significantly correlated (at the99% level) with the MSL at Sydney, but not with the MSL at Norfolk Island, Lord HoweIsland or Auckland. Hence we may conclude that the voltage fluctuations are probablycaused by eddies and associated EAC variations near Sydney, and the annual cycle in thecable voltage may well be related to the seasonal variations of the EAC.

The results from the model also suggest that voltages measured by submarine cablesmay give a useful measure of net transport through a very broad region, provided thatthere are no substantial motions within 300 km or so of the electrodes and that the effectsof chemical potentials and leakage from the earth's core can be estimated or neglected.Unfortunately, the Tasman Sea does not satisfy all these criteria.

Acknowledgements-4he authors are most grateful for comments from Ted Lilley, Nathan Bindoff, JohnChurch, George Cresswell, Stuart Godfrey and Ian Robinson, to Keith Runcorn and Lindsay Molyneux formaking their data available, to R. Legeckis and G. Cresswell for Fig. 2, and to Carol Drew for typing themanuscnpt.

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