Is the South Pacific helium-3 plume dynamically active?

Earth and Planetary Science Letters, 61 (1982) 63-67

63

Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

I31

Is the South Pacific helium-3 plume dynamically active? Henry Stommel Woods Hole Oceanographic Institution, Woods Hole, MA 02543 (U.S.A.)

Received February 23, 1982 Revised version received August 5, 1982

It is suggested that the hydrothermal vents of the South Pacific Rise produce a beta-governed circulation at mid-depth, and that perhaps the associated plume of excess 3He (Lupton and Craig [I]) points westward because of the dynamics of this circulation rather than as a passive tracer.

1. The plume as a passive tracer L u p t o n and Craig [1] have described a great westward pointing plume of excess 3He at a depth of 2500 m whose source, they suggest, is the flux of primordial helium in hydrothermal vents at the crest of the Earth Pacific Rise near 15°S, l15°W. The section displayed by these authors (their fig. 3) is made up of seven stations on an east-west line at 15°S, extending from 9 0 ° W to 134°W. The G E O SECS 3He north-south section of seven stations along 1 5 0 - 1 6 0 ° W seems to confirm the fact that the core 'of excess 3He extends at least that far west, but the spacing of stations is very large (only three in the southern hemisphere). If, following L u p t o n and Craig, we were to regard the plume of 3He as a passive tracer, then we would infer that the direction of the general abyssal flow in this portion of the South Pacific is westward, which would be very different from the •south- and eastward direction called for by the primitive Arons-Stommel model [2]. Evidently some discussion is called for: L u p t o n and Craig's suggestion that topographic effects m a y dominate the abyssal flow seems possible, although we might anticipate that these would lead to flows parallel to the ridge system. Woods Hole Oceanographic Institution Contribution No. 5102. 0012-821X/82/0000-0000/$02.75

A n o t h e r possibility is that the subtropical gyre of the Southern Pacific is extraordinarily deep to the depth of the plume itself--indeed this seems to be visible on the sections shown in Reid's [3] plates.

2. The plume as dynamically active A n o t h e r notion that comes to mind is that the plume seeks to spread westward of its own accord, dynamically, and would do so even in the absence of a general deep flow to advect it. We envisage a thin thermal convective layer, governed by the dynamics of the beta-plane, and driven by heating at the summit of the submarine ridge. In physical terms our suggested view of the plume (Fig. I) is that it is driven by a source-sink doublet over the vents. A flux H of highly heated (about 300°C) water escapes from vents at the ridge. It immediately entrains water at the summit so that a large mass of water at 0.3°C above normal for that level rises to a new equilibrium level about 500 m higher. In the course of the entrainment there is a dilution of a thousand times, so the strength of the source-sink doublet (acting at two levels, source at top, sink at bottom) is 10 3 H. This doublet drives two superposed horizontal gyres, according to the dynamics of the

© 1982 Elsevier Scientific Publishing Company

64

Fig. 1. Two oppositely rotating superposed gyres at mid-depth driven by large volume, we, of water entrained into hot vent water. H, at the lower level and released at higher level. Due to beta-effect the gyres extend westward from the crest of the ridge, with amplitude decaying proportionately to amplitude of vertical eddy-viscosity and associated vertical subsidence wa, between the two levels. The picture is drawn in the southern hemisphere. For comparison with the equations the origin should be moved to the following position: x =0 at eastern edge of ridge; y =0 at equator; z =0 at mid-depth between the two gyres. The two levels are drawn curved to simulate ( - x ) t / 4 spreading of the vertical similarity variable of Gill and Smith [10]. Although current lines are drawn on these levels to indicate the sense of rotation, the full velocity is not tangent to them, but has a component normal to them.

beta-plane: anticyclonic in the upper, cyclonic in the lower, with mass fluxes several times the strength of the doublet. In the absence of vertical mixing the gyres would extend indefinitely far westward, but vertical diffusion of the induced density anomaly causes the gyres to decay westward, and the establishment of a slow d o w n w a r d vertical velocity over the whole center of the plume (between the two gyres) which closes the mass circulation within the plume. The magnitude of the zonal geostrophic transport in the plume should be given by the anomalous density at the central latitude of the plume. The so-called density-break at 2700 m, west of the ridge as shown in fig. 4 of

L u p t o n and Craig [1] has a density deficit of about 20 X 10 - 6 c.g.s, and a total vertical extent of about 500 m. Assuming that this feature of the density field does not extend b e y o n d the equatorward limit of the plume, the zonal geostrophic transports in the gyres would be about 1 sverdrup. If the plume is roughly 1000 km wide in the northsouth direction, the zonal velocities could be about 0.2 cm s - t - - l a r g e enough perhaps to overpower the weaker surrounding abyssal flows, although on a larger scale these eastward abyssal flows must eventually gather up the 3He diffused out of the westward pointing plume and accumulate it to the east of the r i d g e - - a s indeed seems to be observed. This density break has previously been interpreted [4] as a j u n c t u r e of two water masses; therefore it is not certain, by any means, that we can use it to estimate the amplitude of the ventdriven zonal flow as was done above. Because of the great dilution of water from the vent both in the vertical plume, and in the recirculation a b o u t the doublet, a zonal flow of 1 sverdrup ( 1 0 6 cm 3 s - l ) m a y be driven by as little as 3 × 10 -4 sverdrups of hot water from the vents, a n u m b e r which seems to be consistent with geophysical estimates o f the total a m o u n t of hydrothermal heat released in the East Pacific Rise [5]. A c c o r d i n g to visual observations of individual h y d r o t h e r m a i vents from the W.H.O.I. submersible " A l v i n " ( R o b e r t Ballard and John Edmond, personal c o m m u n i c a t i o n ) on the rise near 21°N vent site they average 5 - 4 0 M W each and are arranged single file in the central rift. By Turner's [6] formulae, ignoring possible complications due to the earth's rotation, vents of this magnitude could entrain and raise the ambient stable water by 500 m. If a 0.3-sverdrup flow upward of entrained water is uniformly distributed over a horizontal area (the stippled area in Fig. 1) about 100 km wide (in longitude) and 10,000 k m long (in latitude) along the ridge from equator to pole, there would be a m a x i m u m upward convective velocity wc~ 3 cm d a y - l between the two layers available to drive a planetary flow. This is not very inferior to the amplitude of wind-driven E k m a n p u m p i n g at the surface, although of course the convective driving d o w n not extend over the full width of the ocean.

65 3. The amplitude of perturbation temperature (density) and horizontal velocities over the vents

If we can assume geostrophy over the vents, then the perturbation in temperature O (assuming for a moment that density p = p 0 ( 1 - a8)) is related to northward velocity v by the thermal-wind equation;

3v 38 f-~z = ga-~x

(1)

where f = fly is the Coriolis parameter, x is directed eastward, y northward (and negative in the southern hemisphere). The origin is over the eastern edge of the vents, at the equator, and at mid-depth of the plume. We also assume the vorticity equation:

(2) By eliminating v and integrating over the width of the vent region we obtain an expression for the temperature perturbation Oo(y) at the western side of the vent region in terms of the amplitude of

32w¢/Oz 2 8 ( O , y , z ) - _fly2 f 32w¢ dx ga Jwidth 3Z 2

larger, and approach the magnitude 2 0 × 10 -6 c.g.s, observed in the real density break.

4. The free plume west of the ridge

A very crude model of the plume to the west of the ridge can be constructed by assuming a basic state of abyssal rest with mean vertical temperature gradient (38/3z) and a vertical eddy diffusivity x. This implies an unrealistic downward flux of heat, but has been used as a convenient expedient by various authors. The full temperature is now written as 0(z) + 8(x,y, z) and the linearized temperature perturbation equation is: w "~z

Even if the wc field is independent of latitude, there is a strong parametric dependence of 80 on latitude: it vanishes at the equator; it also vanishes at z levels deeper than the vents and above the top of the convective region. Because individual vents may have differing strengths, lie at various levels, and because we do not know the detailed vertical structure of entrainment and detrainment we can only state roughly that 32wc/3z2~%(max)/H 2 where H is the half-height of the vertically convecting entrainment c o l u m n s - - s a y H = 2 5 0 m. Using f l = 2 × l 0 - 1 3 S - I cm - I , y = - 2 0 0 0 km (corresponding to 20°S) and a = 2 × 10 -4 ° C - i, g = 10 ~ cm s - : (gravity), and a width of I00 km, the amplitude of density perturbation corresponds to a temperature perturbation 80 (20°S)~ 0.02°C (density deficit of 4 × 10 - 6 c . g . s . ) . If the total convection is confined to a narrower range of latitude w~ would be higher locally, and both 80 and the density deficit could be corresponding

(4)

This is applicable only remote from the vents, where the entrainment columns overpower the t¢8,, term. If we eliminate all dependent variables but O we obtain the homogeneous equation: 30

"~ 3x (3)

= K-i~z2

340

- --

3z 4

(5)

where: _

ga

y -- fly2 K

(~--~)

(6)

and where amplitude must be fixed by joining a solution to the values of Oo(Y,z) at the western edge of the vent region. The equation does not contain y except parametrically, so that the y variation of the plume depends essentially on the distribution of the heating along the top of the ridge as a function of latitude and the strong dependence of f on latitude. We can assign values for all the parameters in y except to. From Lupton and Craig [1] the horizontal scale l seems to be about 1000 km, the vertical scale (half plume thickness) h is about 0.5 km, therefore we know "y = I / h 4 = 16 × 10-12 c m - 3 . Usingy = - 1500 km, a~=40× 10 -]~ we find K lies in range 0.2-2.0 c m 2 s - I a value not entirely outside the range of conventionally acceptable values. This equation has been used by Stommel and Veronis [7], Warren [8,9], and similarity solutions of the form 8 ~ ( - ' r / x ) j/4 F ( - y z 4 / x ) (where the function F

66

is bell-shaped with side lobes) have been given by Gill and Smith [10]: that is why the levels sketched in Fig. 1 are drawn as curved at depths of constant values of the similarity variable in the function F, but this detail is not visible in the Lupton-Craig section. Perhaps the plume arises from numerous vents at a variety of levels; or the resolution of the section is not fine enough to detect the similarity form.

plume (z = 0) and driven by convective wc along the line source at x = 0, z = 0 over ridge can be obtained from a single term of a Fourier representation: ~ ( Y ) = ~/~-widthofw°( y )cos nz d x source

where n = ~r/H. According to the equation (3) the perturbation temperature presented to the open ocean west of the vents is:

5. Distribution of 3He and salinity

O(O,y,z)-

This model has a temperature field dominated by linearization about the vertical mean temperature gradient. The corresponding equation for 3He does not contain this gradient, and will be essentially advective in all three components: therefore there will not be a simple parallelism in the distribution of temperature perturbation and 3He in the model. It seems plausible to believe that the helium will be strongest in the westward flowing branch of the upper anti-cyclonic gyre; the maximum dynamical temperature perturbation occurs between the two gyres and is maximum under their central latitude (not under the outgoing branch of the upper gyre). We think that we see this difference in levels in fig. 5 of Lupton and Craig's [1] paper. Reid [11] has identified a tongue of warm temperature anomaly on sigma-3 surface 41.50 pointing westward at about 3000 m and amplitude of up to 0.04°C in the same geographical position as the 3He plume. This is probably associated with the heat from the thermal vent, whereas the larger perturbation in temperature associated with the dynamical density perturbation in the plume is probably invisible on an isopycnal because it is accompanied by a parallel perturbation in salinity from the advection of the mean salinity gradient in the advection-diffusion balance. The perturbation in temperature due to advection of heat from the vent will be visible on density surfaces.

The solution of equation (5) that vanishes at x -- - oo and joins the expression (7) at x = 0 is:

6. Distribution of density, anomaly in the horizontal An approximate idea of the distribution of density anomaly at the level of the central core of a

_

y n2 cosnz ~ ( y ) ga

(7)

O ( x , y , z ) - flY2n: cos(nz)W¢(y) ga × exp(fln'y2Kx/ga~ )

x-~O

-20 i

(8)

-i0 i

O./25

l0

-20

-30

l',

40 Y

Fig. 2. Isotherms (°C) at mid-level in the beta-plume, as function o f latitude and longitude west of the Pacific Rise, due to a line source at the Rise of 10 3 W c m - ~. The vertical diffusivity is t a k e n as 0.1 cm 2 s - j . The l o n g i t u d i n a l extent of the pert u r b e d region is greatest near the e q u a t o r entirely due to the p a r a m e t r i c d e p e n d e n c e of the model on y.

67 I n this expression the d e p e n d e n c e on all p a r a m e ters a n d variables is explicit. O n e of the interesting results of the strong p a r a m e t r i c d e p e n d e n c e of the s o l u t i o n on y is, in the x , y plane, a strong westward p o i n t i n g tongue, even if the vent forcing W ~ ( y ) is i n d e p e n d e n t o f y . A sample set of isotherms at z = 0 is shown in Fig. 2; the a m p l i t u d e is fixed by taking the total power of the line source as 10 3 W c m - I ; a n d we choose r = 0.1 cm 2 s - ~. We think Fig. 2 interesting because it shows that even a u n i f o r m source along the whole length of the ridge produces a p l u m e which in the horizontal plane looks, on the western side of the ridge, like a tongue c o m i n g from a p o i n t source on the ridge. If the vent heating extends right across the equator there will be a m i r r o r image in the n o r t h e r n hemisphere.

7. Conclusions The purpose of this note has been to raise the question: can heating of deep water over the vents of the East Pacific Rise drive a p l u m e d y n a m i cally? Various aspects of the p r o b l e m , a primitive model and working solutions are discussed. It would appear that a positive answer to the question is plausible, if c o m p e t i n g m e c h a n i s m s are not overpowering.

Acknowledgements The a u t h o r thanks W. Jenkins, B. W a r r e n , N.P. Fofonoff, T. Keffer, G. Veronis, J. Pedlosky, J. Reid and J. L u p t o n , a n d some fierce a n o n y m o u s reviewers for helpful c o m m e n t s . T h e work was supported by a g r a n t from the N a t i o n a l Science F o u n d a t i o n No. O C E 15789.

References 1 J.E. Lupton and H. Craig, A major helium-3 source at 15°S on the East Pacific Rise, Science 214 (1981) 13-18. 2 H. Stommel and A.B. Arons, On the abyssal circulation of the world ocean, Parts i and 11, Deep-Sea Res. 6 (1960) 140-154 (Part l), 6 (1960) 217-233 (Part 11). 3 J. Reid, Intermediate water of the Pacific Ocean. The Johns Hopkins Oceanographic Studies Number 2 (The Johns Hopkins Press, Baltimore, Md., 1965) 85 pp. 4 H. Craig, Y. Chung and M. Fiadeiro, A benthic front in the South Pacific, Earth Planet. Sci. Lett. 16 (1972) 50-65. 5 T...I.Wolery and N.H Sleep, Hydrothermal circulation and geochemical flux at mid-ocean ridges, J. Geol. 84 (1976) 249-275. 6 J.S. Turner, Buoyancy Effects in Fluids (Cambridge University Press, Cambridge, 1973). 7 H. Stommel and G. Veronis, Steady convective motion in a horizontal layer of fluid heated uniformly from above and cooled non-uniformly from below, Tellus 9 (1957) 401-407. 8 B.A. Warren, General circulation of the South Pacific, in: Scientific Exploration of the South Pacific (National Academy of Science, Washington, DC, 1970). 9 B.A. Warren, Shapes of deep density-depth curves, J. Phys. Oceanogr. 7 (1977) 338-344. 10 A.E. Gill and R.K. Smith, On similarity solutions of the differential equation q.,,,,: + ~k~ = O, Proc. Cambridge Philos. Soc. 67 (1970) 163-171. 11 J. Reid, Evidence of an effect of heat flux from the East Pacific Rise upon the characteristics of the mid-depth waters, Geophys. Res. Lett. 9 (1982) 381-384.