FEATURE

THE MOON, OF COURSE . .

By Walter Munk and Carl Wunsch

THIS IS AN ESSAY* on tidal friction and pared with 2 × l0 ' GW associated with We now have independent estimates ocean mixing. Tides are not a subject at equator-to-pole heat-flux. of global dissipation from ancient the forefront of current interest. Many eclipses, from modern measurements of oceanographers believe the subject died Astronomy the length of day and month, and from with Victorian mathematicians. But The subject of tidal friction has a long the tidal perturbation of artificial satellite TOPEX/POSEIDON (T/P) altimetry and labored history of errors and miscon- orbits. They all agree within expected measurements have suggested an en- ceptions. Fundamental questions remain error limits. The most precise information hanced lunar role in ocean processes and about the interpretation given in this comes from lunar laser ranging using the put a new face on an ancient subject. In essay. A brief sketch will provide some retroflectors places on the Moon in 1969 contrast, oceanic mixing is alive (even perspective. during the Apollo mission. The semima- fashionable); we wish to convince the In 1695 Halley found that data on an- jot axis of the Moon's orbit is increasing reader that the connection between these cient eclipses could not be reconciled at a rate 3.82 _+ 0.07 cm/y, from which ancient subjects is deep, important, and with his "modern" measurements of the the above dissipation estimate of 2,500 _+ not obviously lunatic. Moon's orbit, and concluded that the 100 GW has been derived. About 100 The reader should hold in mind that Moon was being accelerated by 10 arc- GW is dissipated in bodily tides leaving we are dealing with two quite distinct sec/centuryL This was confirmed by sub- 2400 -+ 100 GW M 2. manifestations of ocean mixing: 1) sequent observations. Euler and La- pehtgic turbulence (away from topogra- grange tried in vain to account for the 3500 GW all tides (1) phy) is associated with a diapycnal diffu- acceleration in terms of Newtonian me- sivity of order KeE = 10 5 mVs and a chanics. The role of tidal friction was The Moon donfinates (and is empha- global dissipation of 200 GW (1 gigawatt proposed in 1754 by Emanuel Kant in an sized in this essay), but the solar tides are = lff' W); 2) the maintenance of abyssal essay "Untersuchung der Frage, ob die by no means negligible. The extension to stratification requires order (2,000 GW) Erde in ihrer Umdrehung um die Achse, all semidiurnal and diurnal tides is com- and is associated with concentrated turbu- wodurch sic die Abwechslung des Tages plex on account of the nonlinear interac- lence at the ocean boundaries and over und der Nacht hervorbringt, eine Veraen- tions (LeProvost and Lyard, 1997). submarine ridges and other topographic derung seit der ersten Zeiten ihres Ur- features, often (improperly) represented sprunges erlitten babe, und woraus man Dissipation in Marginal Seas by a global mean diffusivity of KAS = 104 sich ihrer versichern koennen" (title, not G.I. Taylor estimated tidal dissipation m2/s (1 cgs). abstract). Finally in 1787 Laplace an- of 41 GW in the Irish Sea, using the The subject has the aspect of a zero- nounced that he had discovered the ex- boundary layer formula C D p sum game: we know the global tidal dis- planation: planetary perturbations gave W/m 2 with a drag coefficient CD = sipation quite accurately, 2,500 _+ 100 10.18 arcsec/century ~. This explanation 0.0025. This was in fair agreement with GW for M 2, ~3,700 total, but we do not was considered a major triumph of 18th his independent estimate of 60 GW of know where and by what processes dissi- century science. net horizontal flux

t,d,l W/m 2 into pation takes place. The magnitude is In 1853 Adams found that Laplace and out of the boundaries. Jeffreys ex- comparable with the present global elec- had made an error, and that the correct tended Taylor's estimates to a global tric generating capacity, and tiny as corn- answer was but one-half of Laplace's re- value of 2,200 GW. Since 1920, it has sult, requiring some additional phenome- been taken for granted that nearly all of non (such as tidal friction) to account for the dissipation takes place in the turbu- Walter Munk, Scripps Institution of Oceanography, the astronomical measurements. This was lent bottom boundary layer (BBL) of UCSD, La Jolla, California, [email protected]: rejected because it destroyed a widely ac- marginal seas. Typical tidal currents are Carl Wunsch, Massachusetts Institute of Technol- claimed theory. Not until G.I. Taylor's of the order of 1 cm/s in the deep sea, ogy, cwunsch @ pond.mit.edu. 1919 estimates of tidal dissipation in the and of 1 knot = 50 cm/s in shallow seas. Irish Sea, followed by Jeffreys' and The cubic dependence on tidal current * We cannot give adequate references in this essay and will have to refer to a forthcoming paper Heiskanen's global extrapolation, was velocity leads to the conclusion that by the authors: "The Moon and Mixing: Abyssal tidal dissipation accepted as an important 99% of the ocean accounts for less than Recipes It.'" factor in orbital dynamics. 1% of the dissipation.

132 OCEANOGRAPHY*VoI. 10, No. 3°1997 Most modern tidal models a priori im- community, who had been accustomed to Kd"p/dz-~ = (w - Kt<')dp]dz, (3) pose a 0.0025 p dissipation, with applying a "rigid-lid" surface boundary the conclusion that substantially all the condition on internal waves. with K' = dK/dz. The authors have esti- dissipation takes place in the BBL. This With the use of the appropriate group mated the energy required to maintain the has some of the earmarks of a self-fulfill- velocities, the total internal tide flux from turbulent diffusion as follows: starting ing prophecy. The most recent estimate Hawaii was estimated at 15 GW. Kantha with a global mean p(z) and its first and by G. Egbert (1997) using T/P altimetry and Tierney (1997) have extended this to second derivatives, as compiled from has led to a somewhat reduced BBL dis- a global estimate of 360 GW of M, mode Levitus atlases, a solution to equation (3) sipation: 1,800 GW for M2 (out of conversion, uncertain by a factor of two. yields an expression for 2,400), but he regards the result as very or(z) = [w(z) - K'(z)]/~c(z) (4) preliminary (see also LeProvost and Pelagic Turbulence Lyard, 1997). Measurements of turbulent dissipation Then using very rough guesses about are difficult because of the small scales the upwelling w(z) from circulation mod- Surface to Internal Tide Conversion (down to 1 cm) at which the turbulent els, equation (4) is solved for K(z). The Most of oceanography deals with fluctuations are irreversibly converted global power required to maintain the haroclinic processes, and therefore the into heat. Shear microstructure measure- abyssal stratification is obtained from possibility of surface tidal dissipation by ments were pioneered by Cox, Osborn, equation (2) using K(z). The result is scattering into internal modes is very at- Gregg, Gargett, and Garrett (for recent -2,000 GW, with very large error limits. tractive. The authors have independently discussions see Kunze and Sanford 1996, Egbert's estimate of 2,600 GW for strived in this direction for most of their Lueck and Mudge 1997) . Dissipation is BBL dissipation leaves only 900 GW for career, but were discouraged by the low proportional to N-~(z) over a wide range other losses (Eq. 1). All numbers are ex- numerical estimates of mode conversion. of open-sea conditions, with a propor- tremely uncertain, and the very assump- Extensive calculation by P.G. Baines tionality constant tOpE of ~10 s m-'/s. This tion of the one-dimensional balance (Eq. yielded only 15 GW of mode conversion value is in agreement with remarkable 3) may not provide a useful basis for dis- along 155,000 km of global coastline. tracer release experiments by Ledwell cussion. But there are reasons why such estimates and his associates. The inferred energy might be severely low (as recognized by dissipation is Baines). Mode conversion is proportional e(Z) = "y IKpENZ W/kg (2) to Q-~ where Q is the volume flux across 3.2 0.5 TW the shelf edge. But most of the flux is where 3' = 0.2 is the mixing efficiency. dM~ 251 y parallel to the ocean boundaries, as a Integration of p e(z) over the global 3.7 TW glance at global tidal charts will show. oceans gives 200 GW, a value similar to 3.5 Off-shore ridges do not so constrain the the surface to internal tide conversion. ! I SURFACE TIDES ] flux and are more favorably situated with This suggests that tidal mode conversion I regard to mode conversion. A second rea- is a factor in maintaining pelagic turbu- 3.5 n~rgmal sea~ M'24~ I r~,lze,, ,eam,,unt~, eh son emphasized by Thorpe and Wunsch lence. A possible mechanism is that the (M,- Igt 26. tM cpm 0.9I is associated with the transverse canyons, discrete line spectrum of internal tides is bar,~t I.m /,,tr,,tr,,p, rills, and gullies in the shelf edge that are converted into the internal wave contin- [ IN'rERN~ neglected in a two-dimensional treatment. uum, which in turn feeds the pelagic tur- Interest in the subject was revived by bulence. The remarkable universality ,. H~,,~.,, s ~ 0i2 7 l INTERNALWAVES I some unexpected observational results. (within a factor of 2) of both the fields of ! Dushaw et al. (1995) in an Acoustic To- internal waves and of pelagic diffusivity Localizedi mography triangle deployed 2,000 km has been ascribed to the low fractional Turbulent Patches northwest of Hawaii detected internal I~-~ = 10~mZA dissipation rate of internal waves; Munk I ! 2.6 TW 0-2iFW 0.7 TW 1,0 TW tides radiating from the islands, and this (1997) argues for a more reliable source I was convincingly confirmed by Ray and than just wind energy. Maintenante of Abyssal Stratlficatbm Mitchum (1996) with T/P altimetry. Sur- requires 1.9 TW face manifestations of internal waves Abyssal Stratification have an amplitude of order Ap/p times We now turn to our second subject: Fig. 1: Sketch of the proposed flux of the internal amplitude, or 10 3 × 50 m = mixing implications of the abyssal ocean. tidal energy. The traditional sink is in 5 cm, as measured. Ray and Mitchum ex- Bottom water formation of 25 Sverdrups the bottom boundary laver (BBL) of tracted the semidiurnal tidal components (an uncertain estimate) would fill the marginal seas. Preliminary results from from the three years T/P measurements at ocean basins with dense, cold water in Egbert (1997) based on TOPEX/POSEI- 10-day intervals (hardly in accord with 3,000 years. How is the abyssal stratifica- DON altimet©' suggest that 0.9 TW (in- conventional sampling practice) and tion maintained in the presence of deep cluding 0.6 TW.[or M2) are scattered found coherent waves propagating from convection? along open ocean ridges and at the island chain with wave lengths of Perhaps the simplest model is one seamounts. "Winds" is to include sur- order 100 km, consistent with low-order where vertical upwelling of cold water is face generation of internal waves that internal tides. The detection of internal balanced by downward diffusion from the radiate into the abyss and contribute to tides from satellite altimetry came as a warm surface, as represented by the lin- mixing. Light lines represent speculation surprise to some in the oceanographic ear differential equation with no observational support.

OCEANOGRAPHY'gO]. 10, NO. 3"1997 133 direct measurements of tidal dissipation on ocean ridges, in canyons, and on the continental margins. Off Hawaii, 15 GW of internal tide energy is radiated into the far zone. Could it be that a much larger dissipation is associated with energy --- S-~ , ?,~z trapped in the near zone? In all events, the Moon plays a re- spectable role in the dissipation drama. This has severe implications for past cli- mates when the continental configuration was very different from what it is today; it also raises interesting questions con- cerning the energetics of the modern so- called thermohaline circulation. Twentieth century oceanographers have largely ignored the Moon. Kozma Prutkov is featured in Russian literature as a dumb private in the Czar's army who usually has the right answers (Fig. 2). When asked which is more important, the Moon or the Sun, Kozma replies: "... The Moon, of course, because the Sun shines only in daytime when it is bright anyhow .... "

Acknowledgement W. Munk holds the Secretary of the Navy Chair in Oceanography. Mike Dormer drew Figure 2.

References Dushaw, B.D., B.D. Cornuelle. P.F. Worcester, B.M. Howe, and D.S. Luther, 1995: Baro- tropic and baroclinic tides in the central North Pacific Ocean determined from long- range reciprocal transmissions. J. Phys. Oceanogr. 25, 631-647. Egbert, G.D., 1997: Tidal data inversion: interpola- tion and inference. Progr. Oceanogr. In Fig. 2: The Moon, of course; a pronouncement by Kozma Prutkov. press. Kantha, L. and C. Tierney, 1997: Global baroclinic tides. Progr. Oceanogr. In press. We attach a sketch of the proposed en- of extreme mixing) from which the water Kunze, E. and T. Sanford, 1996: Abyssal mixing: ergy flux (Fig. l), without much hope for masses (but not the turbulence) are ex- where it is not. J. Phys. Oceanogr. 26, 2286-2296. future survival. The notation KAS for the ported into the ocean interior. Le Provost, C. and F. Lyard, 1997: Energetics of diffusivity derived from the abyssal strat- the barotropic ocean tides; an estimate of ification is to distinguish it from KpE asso- Discussion bottom friction dissipation from a hydro- ciated with pelagic turbulence. Typical Our very tentative conclusions are that dynamic model. Progr. Oceanogr. In press. -~- = l) tidal dissipation plays a dominant role values are KAS 104 m:/s and /~PE 10 Lueck, R.G. and T.D. Mudge, 1997: Topographi- m-Ts, and this has led to a discussion of a in pelagic mixing processes and 2) a sig- cally induce mixing around a shallow dichotomy of diffusivities. This may not nificant role in maintaining the abyssal seamount. Science, 276, 1831-1833. be a useful viewpoint. The pelagic value stratification. Munk, W.H., 1997: Once again: once again--tidal is a measure of the distributed turbulent The labored history of the subject has friction. Progr. Oceanogr. In press. Ray, R.D. and G.T. Mitchum, 1996: Surface mani- mixing. We regard KAS as a surrogate for taught us that progress comes from new festation of internal tides generated near a small number of concentrated (almost and decisive measurements. We are Hawaii. Geophysical Research Letters, 23, point) sources of buoyancy flux (region pleased to hear of a number of plans for 2101-2104. []

134 OCEANOGRAPHY'VoI. 10, No. 3-1997