Theory applied to the Mid-Atlantic ridge hydrothermal plumes: the finite-difference approach

Journal of Volcanology and Geothermal Research, 50 ( 1992 ) 161-172

1o 1

Elsevier Science Publishers B.V., Amsterdam

Theory applied to the Mid-Atlantic Ridge hydrothermal plumes: the finite-difference approach M.D. Rudnicki and H. Elderfield Department of Earth Sciences, Cambridge University, Downing Street, Cambridge CB2 3EQ, UK (Received November 20, 1990; revised and accepted June 4, 1991 )

ABSTRACT Rudnicki, M.D. and Elderfield, H., 1992. Theory applied to the Mid-Atlantic Ridge hydrothermal plumes: the finitedifference approach. In: K.G. Cox and P.E. Baker (Editors), Essays on Magmas and Other Earth Fluids (a Volume in Appreciation of Professor P.G. Harris ). J. Volcanol. Geotherm. Res., 50:161-172. A system of differential equations describing the entrainment of ambient seawater during the rise of a buoyant hydrothermal plume has been solved by an explicit finite-difference method, chosen for its ease of application. An equation for tracer concentration has been added so that concentrations in the neutrally buoyant plume can be calculated for those elements whose background profiles vary over the depth range of the buoyant plume. The height of plume rise can be related directly to the thermal and hydrothermal vent flux. For the TAG vent field, 26°N MAR, five plume layers have been identified. The calculated heat flux is 500-940 MW, and the fluid flux is 0.210-0.392 m 3 s-~. The fluid flux to the neutrally buoyant plume is 1460-2740 m 3 s -l. Calculated plume concentrations of Mn compared with measurements made at TAG in 1988 indicate that there is either 50% removal of manganese in the buoyant plume, or that low-temperature vent-fluids contribute about 50% of the total thermal output of the TAG vent field.

Introduction

Submarine hydrothermal plumes are the end result of the interaction between convecting fluid, initially of seawater composition, and hot oceanic crust (Corliss, 1971; Spooner and Fyfe, 1973; Bischoff and Dickson, 1977; Edmond et al., 1979). Hydrothermal systems are not only important for balancing the heat budgets of mid-ocean ridges, but also the chemical budgets for several elements in seawater (e.g., Hajash, 1975; Edmond et al., 1982). Plumes provide the interface between the products of leaching of basaltic rocks and the oceans, and it is through their action that the impact of hydrothermal fluids on seawater composition is effected. Correspondence to: M.D. Rudnicki, Department of Earth Sciences, Cambridge University, Downing Street, Cambridge, CB2 3EQ, UK.

0377-0273/92/$05.00

The plume consists of three regions of interest. Firstly, the vent from which the buoyant fluid emanates. Here, initial fluid properties are important as they define the subsequent behaviour of the flow. Secondly, the rising part of the plume. This is known as the buoyant plume, since it is density deficient. It is here that vent fluid is diluted approximately 10 4 times with ambient seawater, thus changing its pH and other properties, leading to precipitation of minerals and uptake of other tracers through the mixing, or entrainment, process. Lastly, after sufficient dilution, the plume becomes neutrally buoyant, and begins to disperse laterally. This third stage of plume evolution is important for the dispersion of particulate-rich plume material. The study of plumes is important for the study of hydrothermal systems for several reasons:

© 1992 Elsevier Science Publishers B.V. All rights reserved.

162

(1) They provide a means to evaluate the chemical and thermal budgets of a vent field or ridge segment. The process of entrainment integrates the effect of individual sources, so that the chemical or physical anomaly measured in the neutrally buoyant plume is a product of the entrainment history of the rising plume. (2) Chemical behaviour in plumes can modify the impact of hydrothermal fluxes on sea-water chemistry. ( 3 ) The large areal extent of plume material provides a useful prospecting tool to locate areas of hydrothermal activity. In order to use plume properties for these applications, the reactions which take place in the buoyant plume must be evaluated; the mathematical theory of plumes can be used in the analysis. The TAG hydrothermal vent field, at 26°N on the Mid-Atlantic Ridge, has been the target for repeated scrutiny since its discovery by CTD in 1985 (Klinkhammer et al., 1985, 1986; Rona et al., 1986) and study by submersible (Campbell et al., 1988 ). In 1988, it was the focus for RRS "Discovery" cruise 176 (Elderfield, 1988; Elderfield et al., 1988), during which the hydrothermal plume field was mapped using a towed instrument package, and the site of venting accurately located. The site was revisited in 1990 during RV "'Atlantis H " cruise 125 (Mid-Atlantic Ridge Hydrothermal Vents Research Team, 1990 ), when vent fluids and samples from the buoyant plume were collected using the deep-diving submersible Alvin. In this paper, plume theory has been applied to data obtained during these cruises in order to estimate the heat and hot water flux of the XAG vent field. In addition, a method is presented for the calculation of tracer concentrations at the level of neutral buoyancy.

Plume theory The buoyant plume During plume rise, ambient seawater from a range of depths is entrained (Lupton et al.,

M.D. RUDNICKI AND H EI,DERFIELI)

1985; Speer and Rona, 1989; Lunel et ai.. 1990). The chemical and physical composition of the fluid arriving at the base of the neutrally buoyant plume is thus a function of both the vent end-member concentration and flux. and of the background profile of a tracer integrated throughout the depth range of the plume. The amount of seawater incorporated into the buoyant plume at any height is given by the "rate of entrainment" function, (Lunel et al., 1990), a fundamental property of this plume model, based on the mathematical assumption that the amount of entrainment of ambient water into the plume at a given height is proportional to some characteristic velocity of the plume. This was related to the centreline velocity in the 1956 model of Morton, Taylor and Turner (Morton et al., 1956) by a constant, part of the "entrainment assumption". The plume model of Speer and Rona ( 1989 ) can be used to calculate physical properties of the plume at the level of neutral buoyancy, and can easily be extended to calculate tracer concentrations. To their system of equations 1-4), a fifth is added: d(AW) - E A 1!2~/V dZ

] )

d(SAW) - S - E A tl2W dZ

2)

d ( TA W) - T_EA ~I2W dZ

3)

d ( p o A W 2) dZ =g(p~-p)A d( CAW) - C : E A l/2W dZ

(4) (5)

Here, A is the cross-sectional area of a horizontal plume slice, Wis the velocity, Z is the height above the vent, E is the entrainment constant (Morton et al., 1956), Sis the salinity, Tis the temperature, C is the concentration of a tracer, g is the acceleration due to gravity, and p is the density. A subscript z implies a background

THEORY APPLIED TO THE MID-ATLANTIC RIDGE HYDROTHERMAL PLUMES: THE FINITE-DIFFERENCE APPROACH

value measured at height Z, and a subscript 0 implies initial vent conditions. The equations can be incorporated into a matrix solution scheme, replacing derivatives by their explicit forward finite difference representation as follows: dX

Xi+l-X

dZ ~

i

(6)

AZ

The maximum height of plume rise can be calculated from: Zmax =

5B~i4N- - 3 / 4

(8)

following Turner (1973), where Bo is the initial buoyancy flux and N is the buoyancy frequency, given by:

Bo= - g [ a ( T o - T~)

(9)

+ fl(So-S~) lAo Wo

Thus, in matrix form: I

163

W

N = [ - g ( aT" +

0 0 SA ] i S i+' SW 0 AO. 0 o CA //ci+' CZ TA l I T i+l T W O0 AWo AwO Po W2 0 0 0 2 p o A W | I W i+L

___ ]

"AZ(EA ~/:W) +2WA 3Z( SzEA 1/2W) +3SAW AZ( CzEA llZW) + 3CAW flZ( TzEA z/2 W) + 3 TAW AZg(p: - p ) A + 3poA W 2

(7)

m

Here, unsuperscripted parameters represent values at step i; the matrix equation is solved for the values at step i+ 1, that is, at height Z+AZ. Solution proceeds step-wise from measured initial conditions, although it is necessary to scale the independent variable Z so that smaller steps of AZ are taken when plume properties are changing rapidly; that is, initially after venting and also near the height of maximum penetration, Zmax. The background gradients can be either a continuous function of height, or a piecewise linear function; the numerical form of the solution does not require explicit manipulation of this relationship, so its degree of complexity is arbitrary. The matrix can be solved by Gauss elimination or an equivalent method. Calculation proceeds beyond the point where the plume becomes more dense than ambient seawater (neutral buoyancy; commonly referred to as "plume height" ) to the level where its velocity reduces to zero. This additional rise represents plume "overshoot".

lp]

(10)

Here, ~ (--2.13X10 -4 o f - l ) and fl (7.5 X 10-4) are the coefficients of thermal expansion and saline contraction, and are taken from Speer and Rona (1989). Superscripted values represent background gradients. The formula for Zmax (eqn. 8 ) is applicable where background gradients of T and S are linear. The initial heat flux can also be calculated:

AH=poCpATAo Wo

( 11 )

Cp is the specific heat capacity of the vent fluid, given as 6.4 J g- l oC- J by Lupton et al. ( 1989 ) for temperatures >300°C. For a particular field area, the buoyancy frequency N and the vent temperature anomaly 3T ( T o - T~=0) are assumed to be constant. Hence, the equation for the buoyancy flux Bo can be solved in terms of the height of plume rise: _ [ Zma~ 1 ~ Bo --L5N_3/4j

(12)

and, from eqn. 9:

Ao Wo = Bol Ct

(13)

where CI,~--go, AT, and is a constant for a known end-member temperature. This enables vent heat fluxes to be estimated from measurements of background temperature and salinity profiles, plume heights (from nephelometer data), and exit temperatures of hydrothermal solutions. In addition, these results indicate that the observation of layers in a plume above

164

M.D. RUDNICKI AND H. t-StDERFIEI 1)

active hydrothermal vents imply individual or integrated sources of differing fluxes.

The integration of sources and the effect on plume rise It has been stated that plumes integrate sources during rise. The effects of early and later additions of plumes to a model 265 m, 32 MW plume are shown in Table I a-c. Here, the calculated power of a mixed plume, inverted from the model value for Zma~ by the method described above, is compared with the sum of the powers of the individual sources from which it is composed. Calculations show that IABLE 1 Effect on plume height and calculated heat flux of the entrainment of (a) multiple plumes after 1 m of rise; (b) individual plumes at various heights; (c) single plume of varying initial temperature after 1 m of rise. The heat flux calculated from the eventual height of rise of the plume after mixing is compared with the theoretical sum of the beat fluxes of the individual plumes entrained (given in brackets) a, 31ixing (ifplumes 1 m above veto N umber of plumes 2

Application to the TAG area 5

Z~.~t~.~ ( m ) 265 317 400 Z .... ( m ) 350 418 529 3H(MW) 32.0(32.0) 65.3(64.0) 167(160) Error (%) +2 +4

10

479 632 341(320) ~7

Height ( m ) I00

Z , , ~ , , ~ ( m l 320 314 Z .... ( m ) 423 418 AH(MW) 68.5(64.0) 65.3(64.0) Error(%) +7 +2

150

250

291 409 59.8(64.0) --7

260 362 36.7(64.0) --43

c. Mixing with plume o f var.ving initial temperature Temperature ( ~C ) 50 Zneu,ra~ ( m ) 253 Z .... ( m ) 333 3H (MW) 35(34.3) Error (%) +2

Methods The neutrally buoyant hydrothermal plume was m a p p e d in 1988 over a 3' by 3' survey area ( 2 6 ° 0 7 ' - 1 0 ' N ; 4 4 ° 4 9 ' - 5 2 ' W ; vent field located at 26°08.224'N, 44°49.549'W) using a towed CTD package (Neil Brown c"rD MklII), Sea Tech nephelometer, Sea Tech 25cm pathlength transmissometer, and rosette system for collection of water samples fbr subsequent chemical analysis. Acoustic navigation was employed, and the position of the package was recorded every 40 seconds. The precision of the instruments was + 0.001 ~C for temperature, +0.002 for salinity (psu) and + 0.001 m - J for light attenuation. The "nephel" remains an arbitrary unit, but has been calibrated for this dataset against dissolved Mn and particulate Fe in the neutrally buoyant at TAG

[,. Mixing ¢!/2 plumes at different stages o]-plume rise

I0

the early addition of material into the main buoyant plume (Table 1a ) results in a progressive increase in the level of neutral buoyancy, and a predictable increase in the heat flux estimate. The errors in the heat estimates are largely due to rounding errors in the finite difference method. In addition, from Table lb, it appears that heat flux estimates are reliable for addition of material within at least 50% of the height of neutral buoyancy. The effect of the addition of a lower-power source of varying temperature after 1 m of rise is shown in Table l c. The addition of weak, cooler sources appears to affect the eventual height of rise of the integrated hydrothermal plume in a predictable manner, a result which has implications for the entrainment of white smoker and lowertemperature seep fluids ( ~ 40 °C). With these limitation in mind, the problem of calculating the thermal output of a hydrothermal field from high-temperature venting becomes largely a problem of discriminating plume layers from c;rD data.

100

200

300

257 338 37(36.6) +2

265 348 42(41.2) + I

272 357 46(45.8) + 1

THEORY APPLIED TO THE MID-ATLANTIC RIDGE HYDROTHERMAL PLUMES: THE FINITE-DIFFERENCE APPROACH

plume. Manganese was measured on board by oxine pre-concentration and flameless atomic absorption spectrophotometry (Klinkhammer, 1980; Klinkhammer et al., 1985 ); silicate was measured using the silicomolybdate m e t h o d (Strickland and Parsons, 1968 ).

CTD profiles CTD profiles (Fig. la and b) near the site of the TAG venting reveal the hydrothermal plume to be a broad feature of 250 m in thickness between 3450 and 3200 m depth. It is highlighted by anomalies of temperature, salinity and particles. Since the TAG field lies at a depth of 3640 m, this indicates a plume rise of 200-450 m to a level of neutral buoyancy. In all sections where a plume is present, negative temperature and salinity anomalies are observed; that is, it is cold and fresh (Rona and Speer, 1989). The plume is layered; within the layers physical properties are relatively constant, and there is generally an associated particle maximum. Five main plume layers have been identified on this basis, and are denoted in Figure 1a by R o m a n numerals. This particular section was chosen as it was taken very close to the site of venting; in the interpretation below, a nearvent CTD profile is regarded as a snapshot of the vent output, and a similar approach to the calculation of heat and chemical fluxes may be applied to other CTD sections. Layers I-IV have an associated particle m a x i m u m and constant internal temperature and salinity, whilst layer V, despite being associated with a somewhat broader nephels anomaly, again shows constant internal properties over a wider range centred on 3370 m. Three explanations might account for the observation of a layered plume: ( 1 ) that the TAG plume is formed as a broad feature altered by internal convection; (2) that there is vertical diffusion of properties from the original neutrally buoyant solution; or ( 3 ) that the plume is formed in layers reflecting varying source parameters. It has been seen above that the last explanation is consistent with the

[ 65

presence of multiple sources of hydrothermal fluid on the TAG mound. In Table 2, buoyancy flux and heat flux data are presented for the five identified layers. These results are sensitive to the measurement of the temperature and salinity gradients, and thus the buoyancy frequency N; a 5% variation in 5N-3/4 results in a z 20% variation in the calculated buoyancy and heat flux. The parameter 5N - 3/4 is given as 1120 by Speer and Rona (1989). However, from temperature and salinity gradients measured in this study (dT/ d Z ~ 5 . 4 X 1 0 - 4 o C m -~, d S / d Z = 3 . 7 × l O -5 m -~ ), it was calculated to be 957. This leads to a factor of two difference in the estimate of buoyancy flux and, consequently, the heat flux. It is not known whether the observed variation in N is due to temporal variation in (primarily) the ambient temperature gradient, or due to differences in the method of calculation; the 1988 value is the average value for a 25-km 2 area around rAG, and it is known that this gradient is less steep in the immediate vicinity of the m o u n d due to the action of plumes. In addition, To was taken to be 350°C by Speer and Rona (1989) but was measured as TABLE 2 Model results for T A G m a i n plume layers Depth Height (m) Z ...... i ( m )

Buoyancy flux Vent flux B o ( m 4 s 3) AoWo(m3s

t)

Heat flux (MW)

5N 3/4= 1120 3220 3250 3300 3340 3370

420 390 340 300 270

6.00X10 4.47X10 2.66X10 1.57X10 1.06XlO

.-2 -2 -2 .2 -2

0.0798 0.594 0.0353 0.0209 0.0141

192 143 85 50 33

0.2095*

503*

0.150 0.111 0.066 0.039 0.026

360 267 159 94 63

0.392*

943*

5N -3~= 957 3220 3250 3300 3340 3370

*Totals.

420 390 340 300 270

1.13×10 8.38×10 4.99×10 2.94X10 1.98×10

~ 2 2 .2 .2

166

M.D, R U D N I C K I AND H. EL.I)ERFIELI)

Salinity I cmr,craturc

34.910 2.~)

34.930 2.77

Ncphcls 2.5(I 28(X) ..

2.60 I

34.950

34.970 :L 10 2.80

2.93 2.70

r

I

,

~4.930 2.81 2.51

,//'

Tcmpcraturc ...x/(

29(~)

34.910 2.70 2.40

34.950

I

1

: ¢!4

2.63

'. 74

I

I

.Nephels "~

:~,:.,9i(i

2,93 (~a

t

I

Temperature" N / ?

(J),"

/"

3(~X1 } ~ f

3100

Salinity

¢

q

(

I

!

L

,/ j

32(~) (;

"?

(

33(~)

II

4

I

• /

,:

~

if

,

I;'

?

1

34(X) ¢

3500

• k

{6(X)

WOO

(a)

( I

I

:Lea-+

!

I;

I

I

I

Station: 11796-25 RRS Discover), 176/1988

'' /

J

(b) I

t

l

l

~,

i J

Station: 11796-28 RRS Discovery 176/198g

Fig. 1. C T D profiles taken within 50 m of the TAG hydrothermal vent-field. The five plume layers discussed in the text are denoted by roman numerals, and the 3500 m deep plume is indicated.

360-364°C (hence AT=360°C) during submersible operations in 1990 ( R V Atlantis ll/ DSRV Alvin cruise 125, unpubl, data). Thus, - g a A T = - 0 . 7 5 2 , and p C / I T = 2 . 4 x I O 9 W kg -1. These results indicate a total heat output for the TAG hydrothermal field as indicated by the layering in Figure la, of 503-940 MW and a total vent flux of 0.210-0.392 m 3 s -~ , using the different values for N (Table 2), Rona et al. (1990) calculated a heat flux of 120 MW for the main TAG vent complex, using the method of Little et al. (1987 ) from submersible measurements, a result which may indicate that whilst l / 7 to 1/4 of the total heat and fluid flux is from the centre of the mound, a considerable proportion of the hydrothermal fluid at

plume height is entrained from other sources. If an assumption is made about the exit velocity (Wo) of the fluid, then an appropriate value for Ao can be calculated and used in the model to calculate the temperature and salinity anomalies at the level of neutral buoyancy for comparison with those observed. Results for different values of Wo show that the temperature and salinity anomalies are in fact independent of initial I41o values for constant AoWo. This allows a comparison of these anomalies without assumptions of vent exit velocities or radii. The results are shown in Table 3. The model results show good agreement with measured values, but, more importantly, the prediction of greater anomalies with increas-

THEORY APPLIEDTO THE MID-ATLANTICRIDGE HYDROTHERMALPLUMES:THE FINITE-DIFFERENCEAPPROACH 34.910 2.70 2.40

34.930 2.81 2.50

34.950 2.93 2.60

34.970 3.04 2.70

Temperature

\ Salinity

3500mplume

Station: 11796-25 RRS Discovery 176/1988 Fig. 1 (continued). TABLE 3

Calculated and observed temperature and salinity anomalies for the TAG plume

167

from velocity-distance information at each step AZ. Again the calculation appears to be insensitive to both the initial velocity and the height of the plume; for TAG, the time is 36 minutes. Lastly, volume flux and entrainment ratio of material to the base of the effluent layer can be calculated (Table 4), from A and W model results at Z = 0 and Znoutral- The calculated volume flux of plume material to the neutrally buoyant plume above the TAG vent field is 1460-2740 m 3 s -1 using the two values for 5N -3/4 ( 1120 and 957, respectively). The entrainment ratio of end-member fluid actually decreases with an increase in the final level of neutral buoyancy, such that the entrainment ratio for a 420-m plume is 66% of that for a 270-m plume. The average dilution of TAG plume material above the vents before dispersion is ~ 7000 times. The model plume layer fluxes and temperature anomalies (Tables 3 and 4) can be multiplied to give the thermal flux to the neutrally buoyant plume; this value is minus 113-214 MW. This is both a quarter less than, and opposite in sign to, the vent heat flux (500-940 MW). Thus, although Klinkhammer et al. (1986) estimated the TAG heat flux to be 500 MW from the plume temperature anomaly and an estimate of the advecting current, this work would upgrade their figure. Similarly, Speer

Depth

Model

(height) (m)

Observed

Temp. ( ° C )

Salinity

Temp. (°C)

Salinity

TABLE 4

3220(420) 3250(390) 3300(340) 3340(300) 3370(270)

-0.022 -0.020 -0.017 -0.016 -0.014

-0.0062 -0.0057 -0.0049 -0.0044 -0.0039

-0.03 -0.03 -0.02 -0.01 -0.01

-0.005 -0.006 -0.004 -0.003 -0.002

Calculated plume volume flux and entrainment ratios for the TAG plumes

ing plume height is supported by some plume data above the TAG vent field (e.g., Fig. 1a and b) although there appears to be much lateral variation between CTD profiles. The time taken for plume material to reach the level of neutral buoyancy can be calculated

Depth

Volume flux

(m)

(m 3 s -1 )

3220 3250 3300 3340 3370

495-930 392-733 269-503 175-328 132-244 1463-2738 m 3 s f *

*Total.

Entrainment ratio 6200 6600 7600 8400 9400

168

and Rona (1989) have calculated a factor of five mismatch between the equilibrium and vent heat flux for an Endeavour vent field, Juan de Fuca Ridge, plume, with the result that estimates of thermal output based on plume temperature anomalies (e.g., Baker and Massoth, 1987; Rosenberg et al., 1988) need reappraisal. The thermal output of high-temperature vent-fields cannot be estimated simply by measuring the advected heat flux of the neutrally buoyant plume; plume theory must be used to calculate the extent to which the heat flux will be underestimated. 3500-m plume In addition to the main TAG plume described above, a deeper 3500-m plume is present in CXD sections near to the vent field (Fig. l b) and diminished 50 m away to the northwest (Fig. lc). It is typically formed of three or four layers, with associated particle maxima. However, unlike the layers above 3400 m, the smaller plume has a positive temperature (AT,~ + O. 12 °C) and a small salinity anomaly consisting of small spikes of lower-salinity water. These anomalies are non-compensating; the excess temperature is such that the plume must be buoyant. In addition, using the model presented above, a 150-m plume at the level of neutral buoyancy would be expected to have low negative temperature and salinity anomalies. Hence, it is suggested from both the anomalies and the plume model that these layers represent a traverse through a section of buoyant plume. The plume model has been used to calculate the m a x i m u m anomalies expected after 150 m of rise (3500 m depth ) of a 420-m plume. The results predict a model temperature anomaly of +0.17~C and a salinity anomaly of - 0 . 0 0 2 3 , after a rise time of 9 minutes. The anomalies are clearly similar to those measured, although is it intriguing that CTD profiles taken 9 hours and 50 m apart should measure similar deep plumes, but a varied upper plume.

M.D. RUDNICKIAN[)II /IM)ERF1EI./)

Further evidence that the 3500 m anomalies represent rising material for a higher neutrally buoyant plume is presented in Figure I b and c In Figure lb, the 3500-m plume is well defined and has the largest anomalies of temperature. salinity and particles, whereas the anomalies within the core of the neutrally buoyant plume between 3220 and 3350 m are smaller then expected. In comparison, where the 3500-m plume is reduced (Fig. lc), the anomalies in the upper plume are larger. These observations suggest that our profiles have traversed material rising to eventually form plume layers between 3220 and 3350 m. The lower plume has an associated chemical anomaly; sample 11796-33-3, indicated in Fig.ure 2a, has a high Mn concentration character~stic of near-field plume material and was coLlected at 3497 m, 50 m to the northwest of the vent field. For 9 minutes of plume rise, a uniform deep-water current of 9 cm s ~ would be sufficient to bend the buoyant plume over to this extent. Current meter data from ~x(; indicate that this is a good average for currents in the axial valley (Rudnicki, 19901. The observation of buoyant plume material is, again, a useful prospecting tool for the location of active vents. Calculated and measured tracer ratios a~ plume height Whereas the background concentration tbr manganese is constant at 0.2 nmol kg ~ that tbr silicate increases with depth (Fig. 2b) although some plume samples show silicate concentrations below background suggesting reactions within the neutrally buoyant p l u m e Consequently, for silicate, a two end-member mixing model (vent fluid-ambient seawater) is no longer applicable generally (though may be considered as a first approximation, i The model for plume height concentration ot: tracers was applied to manganese and silicate, using the finite difference scheme to integrate the process of the entrainment ofseawater~ with

169

THEORY APPLIEDTO THE MID-ATLANTICRIDGE HYDROTHERMALPLUMES:THE FINITE-DIFFERENCEAPPROACH

(a) 30(X)

r

(b)

I

(c)

!

,

q

~1~\

50% removal

Model

,

Background

• Background

I ~ _

Model

00

~Q m

tn

35(X) I- o /

n I1796-33-3

36(X) ~ n 20

40 Mn

0•

60 80 nmol/kg

,

100

YoungPlume

|

O ratio,2.3 ° 1

?

37(X) " 0

m

-I ]

30

32

.i0

34 Si

36

38

40

-50

-25

0

25

50

M n/DSi

pmol/kg

Fig. 2. (a) Manganese concentrations versus depth, with 100% and 50% model plume Mn concentrations plotted. Sample 11796-33-3 is f r o m the deep 3500 m p l u m e as discussed in the text and may not be c o m p a r e d with the model concentrations for the neutrally buoyant plume. ( b ) Silicate concentration versus depth, with model Si concentrations plotted. Background concentrations are plotted for each element, showing their varying behaviour with depth. (c) Mn/ASi versus depth.

a range of background element concentrations, throughout the rise of the plume. This model makes the assumption that the high-temperature vent fluid end-member has a constant manganese concentration. A difference between the calculated and measured plume height element concentrations could therefore represent either non-conservative chemical behaviour, or mixing with tracer-depleted hydrothermal fluids. The calculated and measured concentrations are shown in Figure 2a and b. It can be seen from Figure 2a that the m a x i m u m manganese concentrations measured are perhaps one half of those calculated at each plume layer. The degree of deviation is given in Table 5. The Mn flux for each plume layer can be calculated from the theoretical fluid flux and the measured Mn concentration for each layer. The total manganese flux (43.8 m m o l s - l ) is 32% of the calculated vent flux of manganese (136 mmol s - I ) . It is important to emphasize that this is an overestimate of the a m o u n t of manganese mismatch since it relies on the measurement of m a x i m u m plume height concentrations, and it is likely that plume waters with higher Mn concentrations were not sampled.

However, it is possible to circumvent this problem by normalising the Mn data to those for the silicate anomaly (LJSi) since silicate is known to remain dissolved in the buoyant plume and behave conservatively (Mottl and McConachy, 1990). The Mn/ASi ratio at the level of neutral buoyancy (Fig. 2c) has a wide range of values, but samples from the young plume (i.e., taken within 1 km of the vent field TABLE 5 Calculated removal of manganese for five TAG plume layers. Total manganese flux to each layer calculated using the lower estimate of the volume flux (Table 4). Total manganese flux to the plume=43.8 mmol s- ~. Total vent flux of manganese = 646/tmol kg-t×210 kg s-1=136 mmol s -~. Manganese removal= (1-43.8/136) × 100%=68% Depth Dilu(m) tion

Concentration (nmol kg - I )

% Volume Mn flux Removed flux (mmol (m3s ') s I)

Model Observed 3220 3250 3340 3340 3370

*Total.

6200 6600 7600 8400 9400

103 97 85 76 70

12 28 44 58 38

88 71 48 24 45

495 392 269 175 132

5.9 11.0 11.8 10.1 5.0 43.8*

170

in the direction of plume advection; RRS Discovery 176 series 11796-9; Rudnicki, 1990) have a value of 12.3 nmol//~mol, which compared with the calculated value of 23-35 n m o l / /tmol. The range of calculated values is a consequence of the difference in entrainment ratios between plume layers. Taken at face value, and assuming silicate is wholly conservative, this comparison either indicates a large degree of manganese removal, with an upper bound of perhaps 50-60%, or entrainment of a high percentage of non-high-temperature endmember vent fluid. Early removal of a substantial fraction of manganese would downgrade its use as a tracer of the neutrally buoyant plume, although the measured manganese concentration in the advecting plume remains 100-200 times background levels. Additionally, quantification of the degree of manganese removal in the buoyant plume would be essential for the understanding of the behaviour of other elements, since manganese oxide efficiently scavenges many elements, e.g., radium and the rare earth elements. However, it is noted that thus far, no particulate manganese has been found in the TAG buoyant plume or in sediments collected near to the TAG mount. If it is assumed that each plume layer has formed due to the integration of individual plume sources, then the observation of reduced concentrations of manganese at plume height can be explained by chemical variability between these sources, and the uptake of large quantities of non-350°C vent fluid into the plume. This is in part borne out by the heat flux data, which indicates that the most obvious source of high-temperature vent fluid contributes only a fraction of the hydrothermal fluid that forms the buoyant plume. Such a situation complicates the use of end-member chemical data in directly calculating plume height concentrations; in addition, individual vents cannot be taken to represent the apparent end-member chemistry.

M.D. RUDNICKI AND H. ELDERFIELI)

Summary A method has been presented for the calculation of the heat and volume flux from hightemperature venting at the TAG vent field. Calculation of these fluxes is necessary in order to assess the importance of high-temperature venting and its influence on the composition of the oceans, and in the reconciliation of geochemical balances.

Consequences of model results on plume height properties From the results described above, it is possible to draw conclusion about the chemical and physical properties of fluids reaching varying heights above an active hydrothermal vent field. Firstly, observation of plume layers above multiple sources implies variation in volume fluxes between distinct sources, or differing "virtual" vent properties dependent upon the entrainment history of the rising plume. The final level of neutral buoyancy attained is dependant upon this entrainment history; if the entrainment happens within 50% of the height of neutral buoyancy, then a heat flux calculated from this level will directly reflect contributions from all entrained sources. The highest layer plume will have the largest heat flux, the largest vent volume flux (A0 l ~ ) , the lowest entrainment ratio and the largest volume flux to plume height. As a direct consequence of these, the plume will have the largest temperature and salinity anomalies, the highest particle concentrations, and the highest concentrations of chemical tracers, assuming conservative behaviour. From sections of physical properties above the TAG vent field (Fig. 1; Table 3 ), it has been seen that temperature and salinity anomalies do indeed increase upwards, and these appear to be associated with a particle maximum. The water column above "rAG would, therefore, seem to represent an ideal example of a multiply sourced, layered, hydrothermal plume.

THEORY APPLIED TO THE MID-ATLANTIC RIDGE HYDROTHERMAL PLUMES: THE FINITE-DIFFERENCE APPROACH

Hea t flux The total global heat flux ascribed to hydrothermal circulation and convective heat removal, the so-called "missing heat", has been estimated from the discrepancy between the calculated and measured heat flux at midoceanic ridges. Wolery and Sleep (1976) calculated this value to be ~5,1012 W (a fluid flux of 1-3.1014 kg y r - l ) , and it has been found that, to a first approximation, the 3He loss from the oceans to the atmosphere necessary to maintain an atmospheric steady state, coupled with measurements of the 3He/heat ratio in high-temperature vent fluids, agrees with this value which suggested that high-temperature hydrothermal systems are the dominant manifestations of convective crustal cooling (Jenkins et al., 1978). Subsequently, both the fluid flux attributed to high-temperature venting has been downgraded to 0.150 . 3 0 * 1014 kg yr -~, or 10% of the previous estimate (Morton and Sleep, 1985), and measurement of the 3He/heat ratio at other sites of hydrothermal activity has produced a range of values (Lupton et al., 1989). The remaining heat loss needed to balance the missing heat at ridges is thought to be lost via lower-temperature systems at ridge flanks. The heat estimate calculated for the "rAGvent field of 500-940 MW implies that there would be expected to be one TAG-Sized vent field for each and every 5-10 km of the total 55000 km oceanic system of ridges if the total missing heat was lost through high-temperature venting, or every 50-100 km using the lower flux estimate. A chemical survey of the Mid-Atlantic Ridge between the Vema Fracture Zone at 11 °N, and the TAG site at 26°N (Klinkhammer et al., 1985), provided evidence for venting at perhaps five localities, or roughly one vent site every 320 km.

Conclusions The concentration of elements at the level of neutral buoyancy can be readily calculated us-

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ing the finite difference scheme detailed in this paper. This allows measured concentrations to be compared with those calculated for strictly conservative mixing, as an indication of removal or addition in the buoyant plume. The use of a plume model is particularly important where an element has a background profile which varies over the depth range of the buoyant plume, and the effects of plume entrainment departs from a situation of simple two end-member mixing. The use of a plume model is, however, absolutely necessary where heat flux estimates are to be made from temperature anomalies in the neutrally buoyant plume. The plume model can be applied to calculate the theoretical temperature, salinity and chemical anomalies for plume layers which appear to be buoyant, and hence estimate the approximate time and distance from the source.

Acknowledgements The authors would like to thank the Captain and crew of RRS "Discovery" for their assistance during cruise 176. Thanks to C. German, G. Klinkhammer, W. Simpson and P. Taylor for C-rD operations, M. Greaves and A. Mitra for manganese measurements, and L. Godfrey and C. German for silicate measurements. This work benefited from the reviews and helpful comments of Chris German and Gary Klinkhammer. This work was supported by NERC studentship GT4/87/AAPS/11 to MDR and NERC grant GR3/6639 to HE. This is Cambridge Earth Sciences contribution No. 1990.

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