Deep-SeaResearch,Vol 34, No 4. pp 531-546.I98?
Printedin Great Britain
0198-0149/87$3.00+ 0 00
@ 1987PergamonPressLtd.
The relationship betweenoceancurrent transports and electric potential
differencesacrossthe TasmanSea,measuredusing an oceancable
PBrenG. BerNes*and RossRr C. BBr-r-*
(Received4 March 1986;in revisedform 29 September1986;accepted30 September1986)
Abstract-An attempt is made to interpret observationsof electricalpotential differencesacross
the TasmanSeain termsof oceancurrents.This voltagerecord(spanning7r1years)is significantly
correlatedwith the (monthly averaged)mean sea level at Sydney,but not with that at other
locations. A numerical model of the Robinson type for the Tasman Sea region permits the
determinationof the cablevoltagewhich resultsfrom a given oceaniccurrent pattern. Most of the
observedvoltage varianceis probably due to East Australian Current eddiescloseto Sydney.
INTRODU CTION
THB measurementof electrical potential differencesin seawateracrosssubstantial
distancesby meansof submarinecablesand the attempteduseof suchmeasurements
to
infer the water transportacrossthe interveningregionhavea long history,goingback to
Faraday.The basic notion is that as seawatermoves horizontally through the earth's
magnetic field, it generatesa potential difference between the two sides of this fluid
current which is proportionalto the fluid transport;the latter may then be inferredfrom
measurementof this potential difference.In practicethis situationis complicatedby a
number of factors,suchas time dependence,complexgeometry,and the partial shortcircuiting of the generatedvoltage by non-moving conductors such as sediments,
stationaryfluid, and even the earth'scrust and mantle.
An additionaland more seriouscomplicationis the fact that variationsin the earth's
magneticfield will inducecurrentsin the cableand henceproducea signalregardlessof
oceancurrent effects.The situationfor long oceancables(the subjectof this paper) has
recently been summarizedby Mslont et al. (1983). Suchmagneticvariationsmay be due
to solar-relatedfluctuationsin the magnetosphere,
high above the earth, or to telluric
currents caused by motions in the earth's core and the geomagneticdynamo. An
additionalunknown factor is due to the possiblechemicalpotentialsat the electrodes;
changesof this nature will probablyoccur slowly, and will be ignoredhere.
In spite of thesedifficulties,a direct relationshipbetweenoceancurrentsand cablemeasuredelectriccurrentshasbeenestablishedfor a numberof locationsover moderate
distances,most notably perhaps,the Straits of Dover and the Straitsof Florida. The
modelusedto relatethe voltagesto the oceancurrentsrangefrom the simpleexpression
derived by LoNcunr-Htccms (1949) to the elaborate numerical models of RosrNsoN
(1976,1977).
* CSIRO Division of AtmosphericResearch,Aspendale,Australia.
531
532
P. G. BAINESand R. C. BELL
In most locationsthe most prominent componentof the voltagesignalis tidal. Since
the oceantides are reasonablywell-knownin many locations,the cablesignalsmay be
calibrated,but suchcalibrationis not generallyvalid for low-frequencymotions(RonrxsoN,1977).Recentobservationsof the Florida Current by SeNrono(1982)and Lansr,N
and SeNpono(1985)give encouragement
that for cablesof moderatelengththe method
haspracticalvaluefor the measurementof low-frequencycurrents.The interpretationof
voltagesmeasuredwith long oceancablesis more difficult. Whereassimplemodelsmay
be adequateto describethe relationshipbetweenoceancurrentsand cablevoltagesover
moderatedistancessuchasstraitsand channels,more elaboratemodelsare necessary
for
complex flow patterns in large regions.However, the possibilitiesof obtaining some
direct measureof the componentsof the circulationof oceanbasinsare tantalizing,and
the effort seemswell worth-while.To this end, it is necessaryto understandthe factors
contributingto the observedvoltagesignalsas well as possible.
The object of the work describedin this paper is to attempt to interpret the observed
low-frequencyvoltagedata-obtained usinga cablerunningacrossthe TasmanSeafrom
Auckland to Sydney-in terms of oceancurrent transports,and to place limits on the
possiblecontribution of the latter to this voltage signal. To achieve this, we have
constructeda numericalmodel of the TasmanSea region of the Robinsontype, which
enablesthe calculationof cablevoltagesfrom known oceancurrent patterns.
OCEAN CURRENT PATTERNS IN THE TASMAN SEA
Current patternsin the TasmanSeashow substantialvariability and, like the circulations in most oceanbasins,are not well understood.The strongestcurrentsare found in
the deep region to the west of Lord Howe Rise (Fig. 1) where the southward-flowing
o
($
b0
East Longitude
Fig. 1. Topographyof the TasmanSea.Depths are givenin thousandsof metres.
1lth December 198O
152"E
154
15 6 "
15 g o
16 0 "
2g"s
2gos
300
32"
{
34"
g2"
34"
360
360
1 60"
I 500E
152"
I 540
15 6 0
15 g o
Fig. 2. An infrared satellitephotographfrom NOAA-6 showing a typical East Australian
Crirrent configurationoff Sydney.Lighier colour implies colder,water..Note eddy "Maria"
forming by ;pinching off"- Providedby R. Legeckis(NESDIA, U.S.A.) and G. Cresswell.
53s
Ocean current transportsacrossthe TasmanSea
East AustralianCurrent (EAC) occurs.This current flowssouthwardalong the Australian coast with a typical transport of 30 x L06m3 s-l (i.e. 30 Sv) until ii reachesthe
latitude of 32oS,where it separatesfrom the coastin the vicinity of SugarloafPoint [see
GoornBv et al (1980),BoI-aNnand CuuncH (1981)and referencescontainedtherein].
The current is generallylarger in summerthan in winter by up to 50%. The separated
current normallyturns northeastwardand meandersand becomesmore diffuse(Fig. 2).
Warm anticycloniceddiesmay become"pinchedoff" at the southernbend in the current
in the neighbourhoodof Sydneyat a rate of 2 or 3 per year. Such detachededdies
subsequently
havean unpredictablebehaviourand may havea lifetime of a yearor more.
Many of them ultimately becomereabsorbedinto the EAC system;escapesouthward
towardthe southernoceanis rare.
The other conspicuous
featureof the TasmanSeacirculationis the mid-Tasmanfront
between30'S and 34oS,extendingfrom near the Australiancoastto the North Cape of
the North Islandof New Zealandwith a typical transportof 15 x 106m3 s-1.This front
may be seen as an extensionof the EAC system,but it is highly variable with large
meanders(Annnewset al. , 7980)and at timesmay be very weak (Cor-evraN
, 1984). Apart
from isolatededdies,currentselsewherein the TasmanSeaappearto be generallyweak.
To our knowledge,no estimateof the net transportthrough the TasmanSeafrom the
north to southhas yet been given.
THE VOLTAGE
AND MEAN SEA-LEVEL DATA
The data were provided to the authorsin the form of an unpublishedmanuscriptby
Runcorn,Richards,Strensand Molyneux, here after denotedRRSM. The settingup of
the observations
wasdescribedby RuNconN(1964).Although there are extensivedata(7
yearsor more) for threelong cables(Sydney-Auckland,Auckland-Suva,Suva-Fanning
Island), we decidedto concentrateon the Sydney-Aucklandcableand the TasmanSea
region.
Detailsof the datacollectionand processingare describedin RRSM. The voltagedata,
in the form of 29-daymeans,are shownin Fig. 3, and coverthe period from March 1969
to September1976.The choiceof this period has the effect of removingvirtually all of
the effectsof the diurnal and semidiurnaltides from the record. This interestingrecord
showslargefluctuationsof the order of +0.5 V, with periodsof severalmonths.We aim
to determinehow much of this record may be attributedto oceancurrents.
06
04
02
o 0
zn.)
04
06
08
1969
Fig. 3.
19'.10
1971
1972
191)
19'14
1975
Auckland minus Sydney monthly mean voltages (from RRSM-see
1976
text),
536
P. G. BaINes and R. C. Brll
l3
Sydney
12
;
o
+
o
t l
1969
Fig. 4.
1970
1971
1972
1973
1971
1975
1976
Monthly mean sea levels at Sydney corrected for atmospheric pressure,
The voltagerecordhasbeencomparedwith other recordsfor the sameperiod, which
relateto the oceancurrentsof the region.Theseare the monthly mean sealevel (MSL)
records at Sydney (Fig. 4), Auckland, Lord Howe Island and Norfolk Island. The
Auckland record is from March 1969to December 1973 only, and is on the Pacific
side.TheseMSL recordshavebeen correctedfor atmosphericpressure,in that the local
isostaticresponseto variationsin atmosphericpressurehas been removed, and they
provide a crude measureof the oceancurrent activity via the geostrophicrelationship.
Part of this MSL variationwill be due to "steric" changes,which are changesin MSL due
to variationsin the temperatureand salinity of the nearby deep water column. Such
changesin MSL are mostly isostatic(Parruu-o et al., 1955;Grll and NnLen, 1973),
meaning that they do not affect the bottom pressureand hence are not related
(1980)found that 44"/"of the total
geostrophically
to barotropicoceancurrents.CHURcH
variance at Sydney could be described by a linear regressionequation, giving a
correlationcoefficientof 0.75,so that this proportionof the SydneyMSL variancecanbe
taken asisostatic.However,the length of the joint record and the natureof the data do
not justify making a correctionfor this effecthere.
Thereis no significantcorrelationbetweenthe Auckland and SydneyMSL records,or
betweenthe Auckland, Lord Howe Island, Norfolk Island MSL recordsand the cable
voltage record, but the SydneyMSL record and the cable record have a correlation
coefficientof 0.33,which is significantatthe99o/oconfidencelevel (if each29-daypoint is
assumedto be independent).This suggeststhat a substantialpart of the variationin the
cable record is directly related to ocean current patterns in the western part of the
TasmanSea.On the other hand, currentsin the easternpart appearto havelittle effect
on the cable voltage.This is consistentwith the known oceancurrent patternsin the
TasmanSea,as describedin the previoussection.
THEORETICAL
BACKGROUND
The equationsfor the voltageinducedby a time-varyingflow are considerablymore
complex than for a steadyflow. However, if the flow varies on a sufficiently long time
scale, local steady-statemay be assumed.For flow varying with frequency co, the
1976)
conditionfor this to be valid is (SnNnono,l97I;RoarNsoN,
o F. 0. L d <'J.,
(1)
Oceancurrenttransportsacrossthe TasmanSea
537
where L and d are horizontal and vertical scales,p, is the magneticpermeabilityof
seawater and o, its electrical conductivity. For this Tasman Sea situation where
L : 2270km, d - 4 km, this parameter :0.07 for 29-day periods, but -4 for I2-h
periods.Hence the steady-state
assumptionis valid for 29-dayaverages,but not for tidal
frequencies.
If fluid flowswith uniform velocityv alonga uniform channelwith semi-ellipticalcross
section, the voltage differenceAQ between the two sidesof the channelis given by
(LoNcuer-Hrccns, 1949)
A0:
vBrL
1 * o6 Ll(2a-d)
volt,
(2)
where B, is the verticalcomponentof the earth'smagneticfield (in teslas: 70-4G), L
and d are the respectivewidth and maximum length of Jhe channel(in metres),and oand o6 are, respectively,the conductivities(in mho m-') of the seawaterand the semiinfinite medium below the channel.The medium abovethe channel(air) is assumedto
havezero conductivity.In mostoceanicsituationswe havedlL < 1; giventhis, LonguetHiggins further showedthat equation (2) is good when the fluid velocity variesin the
vertical, provided that v is interpretedas a vertical averageof the horizontalvelocity.
In practice, particularly when long horizontal distancesare involved, v will vary
substantiallyin the horizontal, the geometry cannot be well-describedas a uniform
channel,and the conductivityin the surroundingmediumis not uniform. Consequently,
more sophisticated
modelsare required.Suchmodelshavebeendevelopedby RonnsoN
(1976,1977)and we follow his procedureshere.
Robinson'smodel is basedon the result that, in steady-state,the observedvoltage
difference A$ betweenthe two electrodesmay be expressedas
AO-- |"w . v dv,
(3)
wherethe integralis over the wholevolumeof the fluid, v is the vectorfluid velocity,and
W is a vector which dependsonly on the geometryof the system,the conductivityof the
seawaterand surroundingmedium, and the magneticfield. This result, establishedby
Bsvtn (1970), may be obtained from the steady-stateequationsof magnetohydrodynamics,namely
j=-oVO+ovXB,
v'j=o'
(4)
where j is the electriccurrent density. In the presentcontext we considera situation
where a unit of currentis passedfrom one electrode(1) to the other (2) with the fluid at
rest, and denotethe corresponding
currentdensityand voltagebyj" and $u, respectively.
Thesequantitieswill satisfythe equations
j,:-oV0,,V.j,:0,
(5)
outsidethe electrodes.Ifj and $ denotethe current densityand potentialcausedby the
fluid motion and hencethey 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 denotesall spaceexcludingthe electrodes,and 51,52denotethe surfacesof the
electrodes.We alsohave
J s , i ' a s : 0 :J s , i ' d s ,
-[s,i, ' 65 : -Js,j, ' dS : L'
(7)
from equations(5) and (6). Then, sincein eachsituationthe potentialis constanton each
of the (relativelysmall) electrodes,we have
0, _0, : -[u0, . vo_j . v0,)dy
:-JvoV0".vxBdV
(8)
which is equation(3) with W : B x i,.
Hence the cablecircuit observesa spatiallyand directionallyweightedaverageof the
whole velocityfield, with the strongestweightingin the regionof oceanin the vicinity of
the cable. This expressionfor the voltage as an integral gives the model a certain
robustnessas a measureof total transport.
THE NUMERICAL MODEL
If W is known, the voltageinducedby a given velocity field may be calculatedfrom
equation(3). The first problemis to determineW : -oB x V0, by solvingfor Su,with a
unit current passedbetweenthe electrodesand ignoringthe cable.
In the TasmanSearegion (Fig. 1) the model employed1'Cartesian grid resolution
whoseboundarieswere placedat26oS,49"S,141"8and 184"E: 176'W (Fig. 6). This
givesa 45 by 25 grid, includingpoints outsidethe boundary.The conductivitystructure
beneaththe TasmanSearegionis poorly known and is probablyrather complicateddue
to the presenceof submergedcontinentalfeaturessuch as the Lord Howe Rise and a
long-defunctspreadingzone, the Dampier Ridge (vaNnen LINDEN,1969).For want of
somethingbetter we assumedthat the conductivitywashorizontallyuniform, and for the
vertical structurewe usedan approximation to the profile obtainedby Fn-loux (7977)tor
the northwestPacific(Fig. 6a). A simplifiedversionwaschosenas a basisfor the mode(Fig. 6b). The variabledepth of the oceanand the disparatethicknessof the layersof
constant conductivity create difficulties for numerical computation. These have been
circumventedfor the calculationof $,, by assuminga top layer of uniform thickness.of
7.7 km incorporatingseawater,sedimentand part of the crust,with a spatiallyvarying
conductivitywhich is a verticalmeanover this distance(usingthe profile in Fig. 6b). This
approximationis justifiablebecausethe horizontal length scalesare much larger than
7 .7 km; consequentlythe resistanceto electricalcurrentsin the verticalin this composite
layer is much smaller than that to horizontal currents, and the layers behave like
conductorsin parallel.In other words, the variation in voltage$, through the depth of
this compositelayer is small.The conductivityof this layer is givenby
ot =
1
(o* d**
o" d" + o, dr),
(e)
4
where the subscriptsw, .sand c refer to seawater,sedimentand crust,respectively,with
539
Oceancurrenttransportsacrossthe TasmanSea
Dr : d* + d, + d, : 7.7 km. The model containsthree lower layers,and their thicknessesand conductivitiesare shownin Fis. 6c. With this grid the equation
V ' ( o V $ " ): p
(10)
is then solved,with oV$" : 0 on the boundariesand p zero everywhereexceptat the
sourceand sink points at the locationsof the endsof the cable,where p : +IlLxLyL,z.
The solution for $, was obtainedby the following procedure.Firstly, an initial guess
for $ wasfound from an inversesquaredistributionaboutthe sourceand sink. From this,
the approximateelectriccurrent field from the topmostto the secondlayer was found.
Using this field as a forcingterm, an exactsolutionfor S in the upper layer wasobtained
by the method of LrNrzeNand Kuo (1969),and an approximatesolution for $ in the
line over relaxation(SLOR-see for exampleAues,
other layerswasfound by successive
b \ o
Fig. 5. Topography of the TasmanSearegion.asusedin the model, showingdepth contoursin
metres.
o lS n-rl
lo-t
to-2
ro-t
loo
T
77 km
o=33
200
300
400
- 500
E
5 600
f 700
o=0002
87 km
o = 0002
513km
o = 0 002 60km Crust
60 km
O = UUT
I
(a)
tb)
(c)
Fig. 6. (a) Electricalconductivityprofile proposedby Frlloux (1977), basedon magnetotelluric data from the northeast Pacific. (b) An approximation to the electrical conductivity
proposedby FILLoux (1977)shownin Fig. 7a. (c) The layers used in the model, approximating
thoseof Fie. 7b.
540
P. G. BnrNrs and R. C. Bell
(o)
(b)
l
l
t l
t l
t l
.
.
.
.
r
t
.
t
l
t
l
l
l
t
l
l . i r l l
r , l l l l
l t l r l l
;
l
l
l
l
l
t
t
,
t
r
t
l
,
r
t
r
,
.
,
t a r t t t . .
t , l r t . . . .
I
t .
I
l t r
t
. .
t
:
t
,,
I
I
t
r
a u a
a a -
r , t . .
: n! t ft' t
.,.,..'"
t \
{{
1t
I
I
l t r t l1
I t fl r I
I
I t t t I
t I t t I
r I l t r
Fig.7. (a) The virtual currentfieldj,, in the seawaterobtainedby passingone unit of current
from Sydney to Auckland. (b) The weighting function W = B x i,. (c) Wd, the W field
integratedover the depth d of the ocean.
Oceancurrent transportsacrossthe TasmanSea
541
1969).A new vertical electric current field wascomputedfrom this new $, and the whole
solutionprocesswasrepeateduntil convergence
of the solutionwas obtained.About 30
iterationswere requiredfor 4-figureaccuracy.We then havej, : -6* V Q" in the ocean;
and W : B x ju, wherethe earth'smagneticfield wasobtainedfrom BaRRacloucHand
MarIN (1971).The cablevoltagefor a given velocityfield is then given by equation(3),
where the integralis taken over the whole body of seawater,usingthe depthsshownin
Fig. 5. The vectorfieldsj,, and W are shownin FigsTaandb, respectively.Note that these
are strongestin the vicinitiesof Sydneyand Auckland, and hencethat the cable signal
shouldbe most sensitiveto current fluctuationsin theseregions.
Figure 7c showsthe integral of W with respectto depth. Here the significanceof the
"Auckland end" is substantiallyreducedbecauseof the shallowdepthsin the eastern
portion of the TasmanSea. Consequentlymuch larger barotropicvelocitiesthan in the
Sydneyregion are requiredthere in order to have the samemagnitudeof effect on the
cablevoltage.
INFERENCESFROM THE NUMERICAL MODEL
The model describedabovehasbeenusedto calculatethe cablevoltageproducedby a
numberof oceancurrentpatternsin the region.Sinceonly barotropiccurrentsaffectthe
cable signal,thesecurrent patternswill be specifiedas verticallyintegratedtransports.
We can define coordinatesx (eastward)and y (northward) where x1(y) denotesthe
Australiancoastlineor the left-handboundaryof the model, andx2$t) the New Zealand
coastlineor the right-handboundaryof the model. For uniform north-southflow where
the transport is independentof x, the model givesan overall transport of 197Sv V-1,
southwardsfor positivevoltage(Auckland relativeto Sydney).The meancablevoltage
over the period of observationis -0.17 V, which would correspondto 34 Sv, northward.
This figure is comparablewith the observedsouthwardtransport of 30 Sv in the East
AustralianCurrent, and would imply a uniform velocityof -0.4 cm s-l. The directionof
this net transport(northward)is consistentwith the "classical"belief manifestedin the
atlasof Schottof 1942(DenaNr, 1961;NeurraeNN
and PrERSor.r,
1966,p.424), although
there has not been any suggestionof a northward transportof this magnitudethrough
the TasmanSeafrom conventionaloceanographic
observationsand it is probablymuch
too large, as discussed
below.
The figure of 197Sv V-r for uniform flow may be comparedwith the corresponding
result from the Longuet-Higginsformula (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) gives
191Sv V-r, which is consistentwith the cable result. However, this agreementmay be
partly fortuitousfor the following reasons.Firstly, the model assumes(effectively)zero
conductivityat depths below 127.7km; in practice, electric currents are expectedto
penetratedown to depth of order L (2270km), so that the model would overestimate
A$. Estimatesbasedon simplecircuit theoryshowthat this error shouldbe smallbecause
of the inhibitingeffectof the low-conductivitycrustlayer.Secondly,W doesnot vanishat
the lateral boundaries of the model, implying an overestimate for A$ due to the
horizontaltruncation.The agreementwith equation(2) may be partly attributableto the
mutual cancellationof these two effects.Taken jointly, these considerationsare not
regardedas seriousdeficiencies.The numericalmodel may thereforebe usedwith some
confidenceto investigatethe effect of non-uniform current patterns on cable voltages,
taking into accountthe variablebottom relief and the conductivityprofile.
<n1
Berurs and R. C. Brr-l
It is possiblefor the cableto registervoltageswith no net north-southtransportat all.
To take a simple example we define a line x3$) by
xz!):
(11)
x{J) + c{x2(y)-xrj))
and a north-south velocity v by
d.v: c2l(40)-xt(y)), * <xt(y),
: c2l(4$t)-xzj)),
(12)
x> xt(y).
with east-westvelocityu : 0, wherec1,c2?ta constants.The flow is oppositelydirected
on each side of .r3Q), with zero total north-south transport (shown schematicallyin
Fig. 8a). If c2is chosento give a transportof 50 Sv on eachsideof x3, with v positivefor
x I x3,the cablevoltagesobtainedfrom the model are shownin Table 1. Theseresults
show that a narrow, strong streamis lesseffectivein generatinga cablevoltagethan a
broad weak one with the sametransport.This is becausethe voltagegeneratedover a
short distanceis more easilyshort-circuitedthrough the deep underlyingmedium than
the voltagegeneratedover a larger distance.Hence,cablevoltagesmay be producedby
east-westasymmetryin the north-southcurrent,and the largerthe asymmetrythe larger
the voltage.If the movingfluid is assumedto havea northwardvelocitywhich is uniform
with longitude (x) (rather than uniform transport), the cable voltage for 33.5 Sv is
(b)
xr(y) x3(y)
x ' ( )y
xly)
xr(y)
xly)
x1(y)
xlv)
of TasmanSeaoceancurrentpatternsstudiedin the model.
Fig. 8. Schematicrepresentation
x1$) and.r2(y) denote the westernand easternoceanboundariesof the model. (a) Uniform
north-southtransport;(b) largeeddy pattern (m = I, n : 2); (c) East AustralianCurrent and
mid-Tasmanfront; (d) eddy near Australiancoast.
Table 1.. Cable voltagesobtainedfrom the model with theflow pattern given by equation (12)
c1
Voltage
0.1
-0.124
0.2
-0.072
0.4
-0.027
0.5
0.011
0.6
0.009
0.8
0.057
0.9
0.113
Oceancurrenttransports
acrossthe TasmanSea
-0.15 V, slightly less than the uniform transport figure of 4.I7 V, and this may be
attributed to the effect of non-uniformityin transportdue to the variationsin depth.
The effect of large-scaleflow patterns may be demonstratedby taking a transport
streamfunction (du : -}yldy, dv : dy/Ox)
V :,.
rin (
mn(x - x{y)
) srn c4y,
xz9) - x{y) t /
(13)
where m is an integer and the origin for y is at the southernboundary of the model
(49'S). We take cq: tt. 3.533x 10*7m-l with n an integer to give integral halfwavelengths,and choosecr : 50 x 106m3 s-1.This representsa doubly periodic cellular flow patternwith a transportof 50 Sv in eachcell (Fig. 8b). Although the transportsin
theseeddy patternsare large,the voltagesare generallysmall(<0.1 V) (Table2). Hence
large-scaleflow patternswith zero net north-southtransportonly havea small effecton
the cablevoltage,even at large amplitude.
Another flow pattern examined was that of a 200 km wide (2 grid points) East
Australian Current with a transportof 30 Sv adjacentto the coast.This current flowed
southwardto the latitude of Sydney,where it turned due eastwardto the North Capeof
New Zealand,representingthe mid-Tasmanfront (Fig. 8c). This flow patternresultedin
a very smallcablevoltageof +0.019V.
Finally, we consideredthe caseof an eddy near the Australiancoast.We assumedan
eddy structurewhich consistedof rigid rotation within a circleof radiusa, with potential
flow outside.The azimuthalvelocityfor an isolatededdy is then
v:ruo) 0<r<aJ
: a2alr,
r>
(i4)
a)'
where r is the radialdistancefrom the centreof the eddy and o is the angularvelocity.If
we approximatethe nearbycoastlineby a straightrigid verticalboundary,we may satisfy
the conditionof zero normal flow there by introducingan imagevortex. If the vortex is
centredat (x,, y,) (at a distancegreaterthana from the coastline)and the imagevortex is
at (x1,y), the transportstreamfunction is given by
\r:f
( @ - * , ) ' + 0 - y , ) 2 - a 2 ) - a 2 i . l l n( ( ( x- * , ) ' *
(x - x")2 +
(y-y,)')Ito),0 < r1e,
rl'
#),
(r-*)'+(y-y)'/'
(1s)
With a radiusa : 100km and an angularvelocityorchosenso that the transportaround
Table2.
Cablevoltagesobtainedfrom the model with theflow
pattern given by equation (13)
X
1
1
2
4
6
0.012
0.019
0.025
-0.006
-0 153
-0.193
0.074
0.059
-0.038
-0.027
0.103
-0.015
544
P. G. Berres and R. C. Bpll
Table 3. Voltages obtained from the model for an eddy
describedby equation (15) with a circular transport o/ 30 Sv
within a radius of 100 km. The eddy centreis locatedat grid
point (i, j); Sydneyis at (12,17)
,\
79
18
t7
t6
15
13
I4
15
0.84
0.44
-0.37
-0.013
0.22
-0.41,
0.20
0.023
-0.014
0.014
-0.29
-0.019
-0.073
An eddy locationover land.
the eddy for r ( a is 30 Sv, the cablevoltagesfor a varietyof eddy locationsare givenin
Table 3. Theseare substantialif the eddy is closeto Sydney,and may have either sign,
dependingon the positionof the eddy.Although the resolutionof the numericalmodelis
too coarsefor eddiesof this sizeto be resolvedwith greataccuracy,Table 3 indicatesthat
the voltagevariationsof the magnitudeof those observed,and of either sign, may be
causedby eddies of realistic size and circulation when they are sufficientlyclose to
Sydney.
We alsonote that the effectsof more complexflow patternsmay be obtainedby superpositionof the abovepatterns,becausethe relationshipbetweencablevoltageand fluid
transportis linear.
SUMMARY AND DISCUSSION
The results from the previous section show that the low-frequeny cable voltage
variationsmay be affectedby oceancurrentsin severalways: (i) by a net north-south
transport through the Tasman Sea at a rate of 197Sv V-1; (ii) by an asymmetric
distributionof the north-southflow with no net transport,and (iii) by significantmotion
suchas eddiesnear the locationsof the electrodes.A simpleinterpretationof the mean
voltageof -0.17 V (Auckland relative to Sydney)implies a net northward transportof
34 Sv, which could be achievedby a meanvelocityof about0.4 cm s-1.However, apart
from a very narrow channel(near Cato Island), the TasmanSeais closedat its northern
end below a depth of approximately1000m by a broad ridge (the Lord Howe Rise).
Hydrographicdata, e.g. the "Eltanin section" at 28'S (platesI and II of Srovvrl e/ a/.,
1973),indicatethat the deeperwater doesnot flow over this ridge, so that any significant
north-south transportmust occur in the upper 1000m. This is the depth range of the
East Australian Current and the mid-Tasmanfront, which togetherpresenta barrier to
northward flow in the westernand centralpart of the upper TasmanSea.This implies
that any northwardtransportmust occur in the easternpart towardsNew Zealand,but
largeand persistentnorthwardvelocitieshavenot beenreportedhere.Further, evidence
from drifting buoysin the TasmanSea,droguedat variousdepthsdown to 200 m, show
no evidenceof systematicnorthward motion (G. Cnesswell, private communication).
Finally, theoreticalmodelsbasedon Sverdruptransportwith realisticwind stressalso
show no substantialnorthward transport in the Tasman Sea (S. GoorREy, private
communication).One is forced to concludethat the net north-south transport in the
TasmanSeamust be substantially<34 Sv, and that the mean cablevoltase must have
Ocean current transportsacrossthe TasmanSea
545
someother cause.There appearto be three possibilities.Firstly, the unknowneffectsof
chemicalpotentialsat the electrodesmay well produceeffectsof order 0.1 V; secondly,
the eddiesnear Sydneymay producea rectifiedeffect of this magnitude,and thirdly, it
may be due to leakageof electriccurrentsfrom the earth's core, as hypothesizedby
RunconN (1964).
The effects of a variety of different flow fields on the cable voltage have been
investigatedwith the numericalmodel,but the only realisticflowswhichwerefound to be
capableof producingthe largevoltagefluctuationsobservedwere eddiesand associated
currentsnear Sydney.Similar effectsnear Auckland are unlikely becausestrong currents
would be necessarythere becauseof the shallowerdepth, and these have not been
observed.Furthermore,the cablevoltagefluctuationsare significantlycorrelated(at the
99% level) with the MSL at Sydney,but not with the MSL at Norfolk Island,Lord Howe
Island or Auckland. Hencewe may concludethat the voltagefluctuationsare probably
causedby eddiesand associated
EAC variationsnear Sydney,and the annualcyclein the
cablevoltagemay well be relatedto the seasonalvariationsof the EAC.
The resultsfrom the model also suggestthat voltagesmeasuredby submarinecables
may give a useful measureof net transportthrough a very broad region, provided that
thereare no substantialmotionswithin 300 km or so of the electrodesand that the effects
of chemicalpotentialsand leakagefrom the earth'score can be estimatedor neglected.
Unfortunately,the TasmanSeadoesnot satisfyall thesecriteria.
Acknowledgements-4he authors are most grateful for comments from Ted Lilley, Nathan Bindoff, John
Church, GeorgeCresswell,Stuart Godfrey and Ian Robinson,to Keith Runcorn and LindsayMolyneux for
making their data available,to R. Legeckisand G. Cresswellfor Fig. 2, and to Carol Drew for typing the
manuscnpt.
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