ISSN 1028334X, Doklady Earth Sciences, 2011, Vol. 439, Part 2, pp. 11791182. Pleiades Publishing, Ltd., 2011.Original Russian Text S.V. Prants, M.Yu. Uleysky, M.V. Budyansky, 2011, published in Doklady Akademii Nauk, 2011, Vol. 439, No. 6, pp. 811814.

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On March 11, 2011, reactors of the FukushimaDaiichi NPP on the eastern coast of Honshu Islandwere disabled as a result of a strong earthquake inJapan and the subsequent tsunami. In addition to theradioactive pollution of the air, the waters were alsopolluted by radionuclides thanks to drainage of waterfrom the NPP reactors, to the radioactive fallout onthe oceans surface, and to the raininduced wash offfrom the soil of the radioactive substances into the sea.Measurements in the sea performed during the firstdays and weeks near the NPP revealed the occurrenceof high concentrations, mainly of iodine 131 (halflifeT1/2 = 8 days) and cesium 137 (halfdecay T1/2 =30.2 years). On March 2930, the concentrations ofcesium 137 and iodine 131 as high as 47 000 and180 000 Bq/l were recorded, respectively [1]. Beforethe disaster, the level of concentration of cesium137 ranged from 1 to 3 Bq/l, while iodine 131 was notdetectable at all. The goal of the present study isnumerical simulation of the polluted water propagation in the ocean as a consequence of the FukushimaDaiichi NPP failure on the basis of the altimetricvelocity field reconstructed from satellite measurement data for the period from March 11 to April 24,2011. To do this, we use the Lagrangian approach toanalyzing the mixing and transport of a passive admixture in the ocean [2].

We examined the northwestern region of the PacificOcean (Fig. 1). The geostrophic velocity field was calculated from the satellite altimetric data in incrementsof 1/3 in space and one day in time [3] using the subsequent bicubic spatial interpolation and the interpolation in time by cubic Lagrangian polynomials.Largescale circulation in this region arises as a resultof interaction of the strong Kuroshio Current and thecold Hoyashio Current of lesser intensity. This frontalzone is distinguished by the occurrence of eddies ofsynoptic scales and by mixing that is nonuniform incharacter. The waters of the Sea of Japan outflowthrough the Tsugaru strait between the islands of Honshu and Hokkaido.

We solve the equation for the advection of theradioactive isotopes

(1)

where (x, y) are the coordinates of a particle, u and vare the angular zonal and meridional velocities at thesite (x, y). Even though the Eulerian velocity field isrelatively simple (being deterministic, for instance),the Lagrangian trajectories of particles motion can becomplicated in the sense of exponential sensitivity tosmall variations in the initial positions of particles andparameters of the flow. This phenomenon is known aschaotic advection (see reviews [4, 5]).

A clear example of the complicated character ofmotion of the advectionsubjected particles providesthe synoptic map of their drift computed thanks to theintegration of equation (1) for 2.25 106 particles

dxdt u x y t, ,( ), dy

dt v x y t, ,( ),= =

Numerical Simulation of Propagation of Radioactive Pollution in the Ocean from the Fukushima Daiichi Nuclear Power Plant

S. V. Prants, M. Yu. Uleysky, and M. V. BudyanskyPresented by Academician V.A. Akulichev May 6, 2011

Received May 18, 2011

AbstractNumerical simulation of the largescale horizontal mixing and transport of radioactive water fromthe Fukushima Daiichi nuclear power plant (NPP) (14102 E, 3727 N, east coast of Honshu Island,Japan) and the use of the satellite altimetric velocity field in the northwestern Pacific allowed us to obtain thefollowing results. The patch of radioactive water dumped from the NPP propagated eastwards as jets of anextension of the Kuroshio Current. The discovered phenomenon of trapping the radionuclides by stable andunstable manifolds of local synoptic eddies may be harmful for living organisms. If one assumes that pollutionof considerable areas of coastal waters near Honshu Island took place due to fallout of radioactive precipitation with rain, then a part of the radioactive water may be subjected to northbound advection and is mixingunder the impact of stable and unstable manifolds of the tripleeddy system to the north of the NPP. No radionuclide flux from the Tsugaru strait into the Sea of Japan has been found in the surface layer. Nevertheless,there is a small likelihood of their penetration there with a deep counter current and/or due to wind drift.

DOI: 10.1134/S1028334X11080277

Ilychev Pacific Oceanological Institute,Russian Academy of Sciences, Vladivostok, Russia

GEOPHYSICS

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evenly distributed over the region. The shades of grayin Fig. 1 depict the magnitude of the quantity D =

, which is the relative displacement of a particle from its initial position (x0, y0) tocertain final one (xf, yf). In this map, the KuroshioCurrent is well pronounced including meanders andintrusions, its extension, and synoptic eddies. Twolightcolored eddy patches are of particular importance. Their centers occur approximately at the latitude of the NPP and at longitudes 153 E (the mushroomlike eddy) and 161 E (the circular eddy), botheddies being surrounded by darkcolored necklaceshaving a relatively high magnitude of D. This patternexemplifies the ring origination process due to the

xf x0( )2 yf y0( )

2+

meandering of the Kuroshio current and subsequentdetachment of eddies from the main jet.

In addition to D, we calculated the particles' displacements by the cardinal points. In the map of theeastwest displacements (Fig. 2a), the darkcoloredareas designate the westwards displaced particles, thelightcolored ones indicate the eastwards displacedparticles, while the gray shaded areas mark the particles that exhibit no displacement sense for the calculation period. On the map of particle displacement(Fig. 2b) the darkcolored areas designate the southward displaced particles, the lightcolored ones indicate the northward transferred particles, while the grayshaded spots show areas with no definite displacementof particles. These maps provide evidence that the pol

16001400120010008006004002000D

30

35

40

45140130

N

E150 160

Fig. 1. Synoptic map of relative drift of advecting particles in this region. The color shades designate the magnitude of drift D inminutes. The Fukushima Daiichi NPP localization is marked with the sign of radioactivity (x0 = 14102' E, y0 = 3727' N)

40

45N

E

35

30

130 140 150 160(a)

130 140 150 160(b)

Fig. 2. Maps of particle displacements in the eastwest (a) and southnorth (b) directions.

DOKLADY EARTH SCIENCES Vol. 439 Part 2 2011

NUMERICAL SIMULATION OF PROPAGATION OF RADIOACTIVE POLLUTION 1181

luted waters were transported from the NPP mainly tothe southeast. However, there are waters, nearest to thedisaster site, that are able to mix for a long time withhout displacement.

There are hyperbolic regions in the oceans whereparticle motion is governed by the same laws that arevalid in the neighborhood of hyperbolic trajectories inchaotic advection. In most cases, they occur in thenecklaces of eddies of diverse scales being particularlyfrequent between the eddies and on the periphery of jetcurrents. The invariant stable (Ws) and unstable (Wu)manifolds are inherent in every such trajectory [4, 5].As follows from the definition of the Ws, a nearbypatch is transported towards the respective hyperbolic trajectory and tends to contract lengthwise inthe direction of this manifold. When nearing thehyperbolic trajectory, the patch begins to stretchlengthwise to the respective Wu. These manifolds inthe ocean do not manifest themselves in the Eulerian velocity field and are not visible in the satelliteimages of the SST or ocean color, but they determine the character of mixing and transport of water[8, 6, 7, 9, 4, 5, 2].

Figure 3 shows the results of direct numerical simulation of propagation of the radioactive pollutionfrom the NPP in the ocean. We considered the twomost probable scenarios of propagation of radioactivesubstances. The first one simulated propagation of thepolluted water, discharged directly from the NPP inMarch, and formed as a result of washing out of theradionuclides from the soil into rivers entering theocean. The altimetric velocity field in coastal areas iscomputed with errors affected by insufficient accuracyof filtering of tidal oscillations. At a distance of 100 kmfrom the shore, we located a patch of the pollutedwater abeam of the NPP. The patch measured 20 100 km and involved 4 106 particles. We calculated itsevolution from March 25 to April 24, 2011 (Fig. 3a).In the process of evolution, the patchs shape becamesubstantially more complex, it smears and travels eastwards until the polluted water becomes entrained bythe stable manifold of the anticyclonic mushroomlike

eddy (Fig. 1) and begins to wind around the latter.Lengthwise along the Ws, the water rich in phytoplankton and nutrients is transported towards theeddies. It is known that Ws and Wu are the attractors ofa sort for the plankton and fish populations [10]. Inspite of the fact that the concentration of radionuclides in such a large patch is comparatively low, theiraccumulation lengthwise along the invariant manifolds may be damaging for living organisms if theymove lengthwise along the manifolds.

The second scenario was aimed at simulation ofpropagation of the radioactive substances that havefallen out onto the ocean surface as atmospheric precipitation. At a distance of 100 km from the shore, weselected a straight line 1000 km long and calculated itsevolution (Fig. 3b). The particles in the middle of theline drifted mainly to the southeast and were entrainedby the extension of the Kuroshio Current involvingtwo major jets. As for the northern jet, a part of particles is entrained by the Ws of the mushroomlike eddyand winds around it. A small outgrowth of the latterrepresents a part of its Wu lengthwise along whichsome particles leave this eddy. The particles of thesouthern fraction of the line are drifting southwardsinto the open ocean. North of the NPP, there is a tripleeddy system: a large synoptic anticyclonic eddy, asmall anticyclonic eddy two degrees north of the latter,and a mediumsize cyclonic eddy at the latitude of theTsugaru strait. This system has a complicated structureof manifolds which determines the character of mixingand transport of the radioactive water. A fraction ofparticles is captured by the Ws of the large anticycloniceddy, performs several turns around the latter, and iswashed out eastwards lengthwise along the Wu of thiseddy. Other particles are captured by the Ws of thesmall anticyclonic eddy and of the Tsugaru cycloniceddy and rotate around them.

The following results have been obtained thanks tothe numerical simulation of the largescale horizontalmixing and transport of the radioactive water from theFukushima Daiichi NPP and to the use of the satellite altimetric velocity field in the northwestern

40

45N

E

35

30

130 140 150 160(a)

130 140 150 160(b)

Fig. 3. (a) Initial radioactive patch (March 25, 2011) and its appearance by April 24, 2011; (b) evolution of the coastal materialline from March 25 to April 24.

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Pacific. The patch of the radioactive water dumpedfrom the NPP into the ocean spreads eastwards andbecomes entrained by the jets of the Kuroshio Currentextension. The phenomenon of trapping the radionuclides by stable manifolds of eddies, which wasrevealed in our study, may be harmful for aquaticorganisms. If one assumes that pollution of considerable areas of coastal waters near Honshu Island tookplace due to the fallout of radioactive precipitationwith rain, then a part of the radioactive water may besubjected to northbound advection and to mixingunder the impact of manifolds of the tripleeddy system. No radionuclide flux from the Tsugaru strait intothe Sea of Japan has been found in the surface layer.Nevertheless, there is a small likelihood of their penetration there with a deep counter current and/or dueto wind drift.

ACKNOWLEDGMENTS

The authors are grateful to D. Kaplunenko forinformation concerning the satellite altimetric data.

REFERENCES

1. Report de Institut de Radioprotection and de SureteNucleaire. http://www.irsn.fr/EN/news/Documents/IRSN_FukushimaAccident_ImpactonmarineenvironmentEN_ 20110404.pdf

2. S. V. Prants, M. V. Budyansky, V. I. Ponomarev, andM. Y. Uleysky, Ocean Model. 38 (1/2), 114125(2011).

3. http://www.aviso.oceanobs.com4. K. V. Koshel and S. V. Prants, Usp. Fiz. Nauk 176 (11),

11781206 (2006) [Phys.Usp. 49 (11) 11511178(2006)].

5. K. V. Koshel and S. V. Prants, Chaotic Advection in theOcean (Izhevsk, Moscow) [in Russian].

6. M. V. Budyanskii, M. Yu. Uleisky, and S. V. Prants, Zh.Eksp. Teor. Fiz. 126 (5) 11671179 (2004) [JETP 99(5) 10181027 (2004)].

7. M. Budyansky, M. Uleysky, and S. Prants, Phys. D(Amsterdam) 195 (3/4), 369378 (2004).

8. G. Haller and G. Yuan, Phys. D (Amsterdam) 147,352370 (2000).

9. F. Lekien, C. Coulliette, A. J. Mariano, et al., PhysicaD 210, 120 (2005).

10. E. Tew Kai, V. Rossi, J. Sudre, et al., Proc. Nat. Acad.Sci. U.S.A. 106, 82458250 (2009).

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