Modelling he idal dispe sion o Cs and
Pu in he English Channel
R. Pe iaH n ez
Depa amen o F&nsica Aplicada, E.U. Ingenie &naT&ecnica Ag &ncola, Uni e sidad de Se illa, C a. U e a km 1,
41013-Se illa, Spain
Abs ac
A nume ical model o simula e he idal dispe sion o non-conse a i e adionuclides in he
English Channel has been de eloped. The model sol es he shallow wa e hyd odynamic
equa ions and, simul aneously, he suspended ma e equa ion which includes deposi ion and
esuspension e ms. The model conside s ha adionuclides can be p esen in h ee phases:
wa e , suspended ma e and bo om sedimen s. Thus he equa ions whose solu ions gi e he
empo al e olu ion o ac i i ies in he h ee phases mus be sol ed oo. The ans e o
adionuclides be ween he liquid and solid phases has been desc ibed in e ms o kine ic
ans e coe$cien s. The model has been applied o simula e he dispe sion o Cs and
Pu eleased om a nuclea uel ep ocessing plan a La Hague (F ance). The model
gi es a ealis ic es ima ion o he ac i i y le els de ec ed in he Channel. The ansi ime o
adionuclides om La Hague o he Do e S ai has also been calcula ed, using he c oss-
co ela ion unc ion me hod, unde di!e en wea he condi ions.
Keywo ds: Model; Tidal; Dispe sion; Radionuclides; English Channel; Cap de la Hague
1. In oduc ion
A nuclea uel ep ocessing plan eleases adionuclides (Sb, Tc, Cs,
Pu) o he sea a Cap de La Hague, loca ed on he F ench coas o he English
Channel (Fig. 1). Some models ha e been de eloped o simula e he dispe sion o
conse a i e adionuclides ( ha emain in solu ion) in pa o he Channel (Salomon,
Gueguenia , O bi & Ba on, 1988) and in he whole channel plus he sou he n No h
Sea (B e on & Salomon, 1995; Salomon, B e on & Gueguenia , 1995; Janin, 1996).
*Tel.: #34-95-4233669; ax: #34-95-4232644.
E-mail add ess: pe [email protected] (R. Pe iaHnez).
Fig. 1. Compu a ional domain. The s a is La Hague nuclea uel ep ocessing plan . The line is he sec ion
along which adionuclide concen a ions a e ob ained (see Sec ion 3.2). Each uni in he x- and y-axis is
5000 m.
Howe e , hese models wo k wi h esidual ci cula ion (a e aged cu en s) and, as
a consequence, hey can only be used o ob ain he long- e m dispe sion o adionucl-
ides ( empo al scale in he o de o yea s).
Recen ly, Pe iaHnez and Regue a (1999) de eloped a nume ical model o simula e he
idal dispe sion o dissol ed adionuclides in he English Channel. The model sol es
he shallow wa e hyd odynamic equa ions o ob ain he ins an aneous wa e el-
oci ies o e he Channel and, simul aneously, he ad ec ion di!usion dispe sion
equa ion is also sol ed. Model p edic ions we e in good ag eemen wi h obse a ions
in he case o Sb and Tc. The model unde es ima ed he concen a ions in he
case o Cs. This can be due o he ac ha his adionuclide is less conse a i e
han Sb and Tc (IAEA, 1985) and hus pa o he eleased Cs is "xed o he
bo om sedimen . Bo om sedimen s may be a sou ce o adionuclides o he wa e
column when concen a ions in wa e a e low enough o allow he deso p ion eac ion
o domina e abso p ion. Du ing he simula ed pe iod he inpu o Cs was smalle
han some mon hs be o e and hus he Cs con ibu ion om he sedimen could be
highe han he inpu om he sou ce. This e!ec was no conside ed in he model and
could explain he unde es ima ion o he Cs concen a ions.
The objec i e o his wo k consis s o ex ending he p e ious model o non-
conse a i e adionuclides. Thus, he shallow wa e hyd odynamic equa ions a e
sol ed and, simul aneously, he suspended ma e equa ion, which includes ad ec ion
and di!usion o suspended pa icles plus he deposi ion and esuspension p ocesses,
and he equa ions ha go e n he dispe sion o adionuclides in he h ee phases
conside ed (wa e , suspended ma e and bo om sedimen s) a e sol ed oo. The
ans e s o adionuclides be ween he liquid and solid phases a e desc ibed in e ms o
kine ic ans e coe$cien s. The model has been applied o simula e he dispe sion o
Cs: he objec i e is o imp o e he esul s o Pe iaHnez and Regue a (1999). I has
also been applied o s udying he dispe sion o Pu. The dispe sion o his
adionuclide, which has a high a$ni y o he solid phases, in he English Channel has
no been s udied be o e wi h nume ical models. Also, he ansi imes o adionuclides
om Cap de La Hague o he S ai o Do e (see Fig. 1) ha e been calcula ed.
The model is p esen ed in he nex sec ion. The ea e , he esul s a e p esen ed and
discussed.
2. The model
2.1. Hyd odynamics
The wo-dimensional shallow wa e hyd odynamic equa ions a e p esen ed in
Pe iaHnez and Regue a (1999) and will no be epea ed he e. They include he non-
linea e ms, a Co iolis e m and he e!ec o wind. The use o a wo-dimensional
model is jus i"ed due o he dominance o ba o opic o e ba oclinic mechanisms in
he shallow and well-mixed wa e s o he Channel (B e on & Salomon, 1995).
Ins ead o using a cons an alue o he bed ic ion coe$cien , as is usual in mos
models, i s alue has been inc eased om 0.0015 in he wes Channel o 0.0875 in he
Do e S ai o ob ain a be e ag eemen be ween he obse ed and compu ed
cu en s. Indeed, P andle (1975) has ound in p e ious modelling wo k ha ic ion
inc eases in he egion a ound Do e and has no ed ha he alue o he ic ion
coe$cien mus be selec ed wi h ca e in his a ea so as o accoun o such an inc ease
in he bo om ic ion.
2.2. Suspended ma e dynamics
As usual in suspended ma e s udies, we will conside ha only pa icles wi h
a diame e (62.5 lm can emain in he wa e column as suspended ma e , since
la ge pa icles will sink apidly o he bo om and, as a consequence, hei ho izon al
mo emen is negligible (Belde son, 1964; Gu bu , Ke shaw & Du ance, 1987; Cla ke,
1995; Pe iaHnez, Ab il & Ga cmHa-LeoHn, 1996a). Indeed, Eisma (1981) has poin ed ou
ha o all p ac ical pu poses muds can be ega ded as synonymous wi h suspended
ma e . The suspended ma e equa ion is
*(Hm)
* #*(uHm)
*x#*( Hm)
*y"*
*xHKV
*m
*x#*
*yHKW
*m
*y
!wQm1!q
qAB #E q+, (1)
whe e mis he suspended ma e concen a ion in g/m,uand a e he componen s o
he wa e eloci y along he xand ydi ec ions, His he ins an aneous wa e dep h and
KVand KWa e he di!usion coe$cien s along he xand ydi ec ions. The las wo
e ms ep esen deposi ion and e osion o he sedimen . The deposi ion e m has been
based on he concep gi en by Teisson (1991), also used by Cla ke (1995): wQis he
se ling eloci y o suspended pa icles, q"(u# is he cu en magni ude and
qAB is a c i ical deposi ion eloci y. Thus, deposi ion occu s only i q(qAB; o he wise
his e m is se o ze o. Eis he e osion cons an (Nicholson & O'Conno , 1986), Mis
some powe o he wa e eloci y, ypically in he ange 2}5 (P andle, 1997) and gi es
he ac ion o small pa icles (diame e (62.5 lm) in he sedimen . This way, he
o mula de i ed by Fukuda and Lick (1980) and La elle, Moj eld and Bake (1984)
has been used o he e osion a e, al hough he ac o has been included o ake
in o accoun ha only pa icles wi h diame e (62.5 lm can be inco po a ed
as suspended ma e in o he wa e column. E osion occu s only i he wa e eloci y
is la ge han a c i ical e osion eloci y, qAC ; o he wise he e osion e m is se
o ze o.
The se ling eloci y o suspended pa icles, a low concen a ions (smalle
han 1000 ppm), inc eases as he suspended ma e concen a ion inc eases. A
s anda d o mula used o ep esen his p ocess is (Pej up, 1988; Meh a, 1989;
Cla ke, 1995):
wQ"am?

, (2)
whe e aand aha e o be ob ained om measu emen s o om model calib a ion.
Finally, a sou ce e m mus be included in he suspended ma e equa ion along he
coas line. This e m ep esen s he inpu o pa icles om uno!o con inen al wa e s
(Pe iaHnez, 1999).
The solu ion o he suspended ma e equa ion p o ides he suspended ma e
concen a ion a each posi ion in he model domain and a each ins an o ime.
2.3. Radionuclide dispe sion
As commen ed abo e, he model conside s ha adionuclides can be p esen in
h ee phases: solu ion, suspended ma e and ac i e bo om sedimen s (pa icles wi h
a diame e (62.5 lm). I is conside ed ha he ans e o adionuclides om wa e o
he solid phase is go e ned by a coe$cien kand he in e se p ocess by a coe$cien
k, which a e deno ed kine ic ans e coe$cien s. The adso p ion o adionuclides
will depend on he su ace o pa icles pe wa e olume uni . This quan i y has been
deno ed as he exchange su ace (Pe iaHnez, Ab il & Ga cmHa-LeoHn, 1996b; Pe iaHnez
& Ma mHnez-Agui e, 1997a; Pe iaHnez, 1999). Thus
k"s(SK#SQ), (3)
whe e SKand SQa e he exchange su aces o suspended ma e and bo om
sedimen s, espec i ely, and sis a pa ame e wi h he dimensions o a eloci y. I is
deno ed as he exchange eloci y (Pe iaHnez e al., 1996b). As a " s app oach,
assuming sphe ical pa icles and a s ep unc ion o he g ain size dis ibu ion o
pa icles, i can be easily ob ained (Pe iaHnez e al., 1996b) ha
SK"3m
oR, (4)
SQ"3¸ 
RH , (5)
whe e ois he suspended pa icle densi y, Ris he mean adius o suspended ma e
and ac i e sedimen pa icles, ¸is he a e aged mixing dep h ( he dis ance o which
he dissol ed phase pene a es he sedimen ) and is a co ec ion ac o ha akes
in o accoun ha no all he mass o he sedimen is in con ac wi h wa e .
The ans e coe$cien kis conside ed cons an . This desc ip ion o he ans e o
adionuclides be ween he dissol ed and he solid phases has been used success ully in
p e ious modelling s udies (Pe iaHnez, Ab il & Ga cmHa-LeoHn, 1996c; Pe iaHnez
& Ma mHnez-Agui e, 1997aPe iaHnez & Ma mHnez-Agui e, 1997b; Pe iaHnez, 1999).
The equa ion ha gi es he empo al e olu ion o adionuclide concen a ion in he
dissol ed phase, CB(Bq/m), is
*(CBH)
* "(ad #di )!kCBH#kCQmH#kAQ¸oQ ;10!jCBH, (6)
whe e (ad #di ) means ad ec i e plus di!usi e anspo o dissol ed adionuclides,
CQ(Bq/g) and AQ(Bq/g) a e adionuclide concen a ions in suspended ma e and
ac i e sedimen pa icles, espec i ely, he sedimen bulk densi y oQis exp essed in
kg/mand jis he adioac i e decay cons an . The ex e nal sou ce o adionuclides
should be added o his equa ion a he poin s whe e i exis s. The ans e coe$cien
kis gi en by
k"s3m
oR#3¸ 
RH . (7)
The equa ion o he empo al e olu ion o speci"c ac i i y in suspended ma e
pa icles is
*(mCQH)
* "(ad #di )#kCBH#kmCQH#(e os!dep)!jmCQH, (8)
whe e kis gi en by he " s e m o Eq. (7) and he e osion and deposi ion e ms a e
gi en by
e os"E q+AQ, (9)
dep"wQmCQ1!q
qAB . (10)
Again, a sou ce e m should be included in Eq. (8) i he e exis s an ex e nal inpu o
adionuclides "xed o solid pa icles.

The equa ion o he empo al e olu ion o speci"c ac i i y in he ac i e ac ion o
he sedimen is
*AQ
* "k
CBH
¸oQ 10 !kAQ#(dep!e os), (11)
whe e kis gi en by he second e m o Eq. (7) and he deposi ion and e osion e ms
a e gi en by
dep"wQmCQ
¸oQ 1!q
qAB 10 , (12)
e os"Eq+AQ
¸oQ
10 . (13)
2.4. Model conxgu a ion
To sol e he equa ions, a spa ial and empo al disc e iza ion is ca ied ou : he
Channel was di ided in o 3750 g id cells ( o ming a ma ix 75;50). The g id ex ends
om 48.33N o 51.03N and om 4.03W o 1.53E; he g id cell size is
*x"*y"5000 m and he ime-s ep is "xed as * "60 s.
The explici "ni e di!e ence scheme desc ibed in Fla he and Heaps (1975) was used
o sol e he hyd odynamic equa ions. Second-o de accu acy "ni e di!e ence schemes
(Kowalick & Mu y, 1993) ha e been applied o sol e he ad ec ion and di!usion
e ms in he suspended ma e and adionuclide dispe sion equa ions. In he case o
ad ec ion, i consis s o a second o de app oxima ion o he upwind scheme. All he
s abili y condi ions (Kowalick & Mu y, 1993) a e sa is"ed by he spa ial and
empo al esolu ions o he model.
The compu a ional domain is p esen ed in Fig. 1. Along he open wes e n bound-
a y, wa e ele a ions we e speci"ed o each ime-s ep om obse a ions (Howa h
& Pugh, 1983). A adia ion condi ion (Kowalick & Mu y, 1993) is applied along he
no heas e n open bounda y (Do e S ai ). Along he coas , he cu en componen
ha is no mal o he bounda y is se o ze o. Only he wo main idal componen s
(M#S) a e conside ed. Good ag eemen wi h obse a ions is ob ained al hough
only wo componen s a e used, as will be seen.
In he case o he dispe sion equa ions, he e is no #ux o adionuclides o
suspended ma e h ough a closed bounda y. Along open bounda ies, he ollowing
bounda y condi ion is applied:
CG" CG , (14)
whe e CG ep esen s he concen a ion o adionuclides o suspended ma e a he
open bounda y and CG  ep esen s he concen a ion jus inside he compu a ional
domain. This condi ion has been p e iously applied in Pe iaHnez (1998a,b,1999) and
Pe iaHnez and Regue a (1999).
A FORTRAN code was de eloped o sol e he equa ions in ol ed in he model and
was implemen ed on a HP SPP 2000 X-Class compu e .
3. Resul s and discussion
3.1. Hyd odynamics and suspended ma e dynamics
The magni ude and di ec ion o he compu ed and obse ed cu en s ha e been
compa ed o 12 poin s in he channel o sp ing, medium and neap ides. Obse ed
and compu ed Mco ange cha s ha e also been compa ed. Resul s a e, in gene al, in
good ag eemen wi h obse a ions. De ails can be seen in Pe iaHnez and Regue a
(1999) and will no be epea ed he e.
The ollowing pa ame e s a e used o sol e he suspended ma e equa ion: di!u-
sion coe$cien s a e "xed as KV"KW"51 m/s and i is assumed ha "0.9 in Eq.
(14) (see Pe iaHnez & Regue a, 1999, o de ails).
One o he main di$cul ies in sedimen anspo modelling is he me hod o
ob aining he e osion and deposi ion h esholds and he e osion cons an . These
pa ame e s a e speci"c o each si e and hey a e o en selec ed a e a model
calib a ion p ocess. Thus hey a e selec ed in such a way ha hey p oduce he bes "
o he model esul s wi h he obse a ions. O cou se, hese pa ame e s mus be
physically ealis ic.
A e some model uns, he e osion cons an has been "xed as
E"2.2;10  gm
s. Uncon en ional uni s a e due o he ac ha Ealso ac s
as a scaling ac o : he e osion a e mus be exp essed in g m s  and i has been
assumed ha M"3.5 (as commen ed abo e, Mis ypically in he ange 2}5).
I has been selec ed, also a e a model calib a ion, ha a"5.7;10  and
a"1.6 in Eq. (2) is wQis exp essed in m/s and min g/m. Since suspended ma e
concen a ions in mos o he Channel a e o he o de o 1 g/m, se ling eloci ies o
he o de o 10  m/s a e ob ained, which is he o de o magni ude ha can be ound
in he li e a u e (P andle, Jago, Jones, Pu die & Tappin, 1993; P andle, 1997)
o he se ling eloci y o cohesi e sedimen s. Indeed, i can be ound in he li e a u e
ha a anges be ween 0.5 and 2 (Pej up, 1988; Eisma, 1993). A alue o 1.6 was
ob ained by Meh a (1989) and was also used in p e ious modelling wo k (Pe iaHnez e
al., 1996a). I can also be seen ha a anges om 10  (Cla ke, 1995) o 10  (Meh a,
1989).
The c i ical deposi ion and e osion eloci ies ha e been aken om li e a u e da a.
A alue o 0.18 m/s has been used o he c i ical deposi ion eloci y (Eisma, 1993;
Pe iaHnez e al., 1996a) and a ypical alue o 0.21 m/s was assumed o he c i ical
e osion eloci y (Hea he shaw, 1981; Pugh, 1987). Indeed, i has al eady been poin ed
ou (Cla ke, 1995) ha due o he small size o cohesi e sedimen s hey end o be slow
alling and hus he e is some lag be ween he end o deposi ion and e osion begin-
ning. Du ing he in e media e ime in e al, he sedimen suspension is main ained by
wa e u bulence wi h no appa en e!ec on e osion o deposi ion. Thus, usually,
qAB(qAC (Cla ke, 1995).
The suspended ma e sou ce- e m om con inen al uno!was selec ed a e
a calib a ion p ocess. Along he F ench coas , i was conside ed ha a mean supply o
0.027;10kg/yea occu s. Along he B i ish coas i was "xed as 0.35;10kg/yea .
O cou se, uno!will no be cons an h ough he yea , bu hese alues may be
conside ed as annual a e ages ha gi e a mean suspended ma e dis ibu ion o e
he Channel ha is, in gene al, in ag eemen wi h he obse ed ea u es o suspended
ma e concen a ions. Fo compa ison, suspended ma e supply o he No h Sea
om di!e en i e s anges om 10(Ems i e ) o 10kg/yea (Thames plus Hum-
be , Rhine plus Meuse i e s), and he supply om coas al e osion (Eas Anglia plus
Holde ness coas s) is 0.7;10kg/yea (Eisma, 1981).
The mean suspended ma e concen a ions compu ed by he model a e p esen ed
in Fig. 2a and a e, in gene al, in ag eemen wi h hose gi en by Eisma and Kal (1987),
shown in Fig. 2b, ob ained om obse a ions. Suspended ma e concen a ions a e
somewha highe along he English coas (some 5 ppm) han along he F ench coas
(some 3 ppm). Also, suspended ma e concen a ions o 5 ppm a e ob ained o he
no h o La Hague. Un o una ely, he e a e no measu emen s in he wes e n pa o
he Channel ( om La Hague o he wes ). Again, he use o a wo-dimensional model
is jus i"ed since Eisma and Kal (1987) ha e ound ha suspended ma e concen a-
ions in he bo om wa e a e a he simila o hose in he su ace wa e . Measu ed
(B ylinski, Dupon & Ben ley, 1984) and compu ed suspended ma e concen a ions
a Do e S ai ha e also been compa ed: measu ed concen a ions 10 and 15 km
om Cap G is-Nez a e 7 and 5 ppm, espec i ely; he co esponding mean compu ed
alues a e 5.5 and 5.2 ppm.
The suspended ma e #ux h ough he Do e S ai in o he No h Sea has been
compu ed as 1.3;10 g/yea . Eisma (1981) es ima ed a #ux o 1.0;10 g/yea ,
al hough he alue ob ained by Van Alphen (1990), 1.7;10 g/yea , is conside ed he
mos accu a e es ima e (Eisma, 1990). Thus he compu ed #ux is in a he good
ag eemen wi h p e ious es ima es.
3.2. Radionuclide dispe sion
The compu ed dis ibu ion o a conse a i e adionuclide (Tc) in he Channel is
p esen ed in Fig. 3 as an example ( om Pe iaHnez & Regue a, 1999). In he case o
a conse a i e adionuclide, s"k"0. I can be seen ha concen a ions a e
highe on he F ench side o he Channel han on he English side. The banded
s uc u e, showing dec easing ac i i ies o! he F ench coas , has been obse ed by
Gueguenia , He mann, Ke shaw, Bailly du Bois and Ba on (1996) and is also
appa en he e. Wa e s o he No man B e on Gul a e a!ec ed by he discha ges om
La Hague due o he exis ence o gy es a ound he Channel Islands (O bi & Salomon,
1988). The Do e S ai ac s as a bo leneck and hus g adien s a e enhanced in his
a ea. This e!ec was also ound by B e on and Salomon (1995).
Some pa ame e s mus be known o simula e he dispe sion o non-conse a i e
adionuclides. The mixing dep h ¸was aken as 0.1 m, ollowing p e ious modelling
wo ks (Pe iaHnez e al., 1996c; Pe iaHnez & Ma mHnez-Agui e, 1997a; Pe iaHnez
& Ma mHnez-Agui e, 1997b; Pe iaHnez, 1999). The densi y o suspended ma e pa -
icles is aken as 2600 kg/m, which is he es ablished alue o soil pa icle densi y
(Ba e , Ga dne & Ga dne , 1972). The mean adius o suspended ma e and ac i e
sedimen pa icles has been selec ed as R"15 lm, since only pa icles wi h a
diame e (62.5 lm can be p esen in he wa e column as suspended ma e , as
Fig. 2. (a) A e age suspended ma e concen a ions (ppm) calcula ed by he model. (b) Suspended ma e
concen a ions (ppm) om obse a ions o Eisma and Kal (1987).
local se ies, ha is de"ned as
h(q)"1C( )C( #q)2
(1C( )2(1C( )2, (15)
whe e his he c oss-co ela ion unc ion, Cand Ca e concen a ions a La Hague
and he cen al Do e S ai , espec i ely, and 12means ime-a e aging. The max-
imum o he c oss-co ela ion unc ion occu s o a gi en alue o q, which is
a s a is ical e alua ion o he ansi ime be ween he wo poin s.
I wind is no included in he model, he compu ed ansi ime due o ides is 4.1
mon hs. Howe e , i he a e age wind, sou hwes 6 m/s (B e on & Salomon, 1995), is
included, he ansi ime is educed o 3.0 mon hs. This alue is in close ag eemen
wi h he p e ious calcula ion o Salomon e al. (1995) wi h a long- e m model. This
dec ease is due o he ac ha a e age wind condi ions p oduce an inc ease in he
esidual d i o he No h Sea ela i e o he idal d i . This compu ed alue is also in
ag eemen wi h he p e ious expe imen al es ima ions o Gueguenia , Bailly du Bois,
Gandon, Salomon, Ba on and Leon (1994), who ound a ansi ime be ween 2 and
8 mon hs. A ansi ime o 3 mon hs implies an a e age eloci y o adionuclides
discha ged a La Hague o 83 km/mon h. O cou se, he ansi ime depends upon
wea he condi ions. Thus, in he case o a cons an eas e ly wind (speed 6 m/s), he
compu ed ansi ime is inc eased o 7.1 mon hs.
O cou se, ansi imes a e a!ec ed by he eal changing and non-homogeneous
wind "elds. Howe e , ou calcula ions allow easonable es ima ions o he o de o
magni ude o he ansi imes. Indeed, 3 and 7.1 mon hs ha e been ob ained o
a e age wind and eas e ly wind condi ions, espec i ely. The es ima e by Gueguenia
e al. (1994), 2}8 mon hs, ep esen s he eal mix u e o di!e en wind condi ions since
i has been deduced om obse a ions. The calcula ions om his modelling s udy a e
in he ange o a ia ion gi en by Gueguenia e al. (1994) and hus hey can be
conside ed as ealis ic alues.
These ansi imes ha e been compu ed o dissol ed adionuclides, conside ing
ha s"k"0. Howe e , i has been obse ed ha i adionuclides ha e a high
a$ni y o he solid phase he ansi ime inc eases signi"can ly. Thus, in he case o
Pu, he ansi ime o Do e is 7.0 mon hs (in a e age wind condi ions) a alue
ha is highe han he ansi ime o a conse a i e adionuclide by a ac o 2.3. The
ansi ime o plu onium had no been calcula ed p e iously.
4. Conclusions
A model o simula e he dispe sion o non-conse a i e adionuclides in he English
Channel has been de eloped. The model sol es he shallow wa e hyd odynamic
equa ions, he suspended ma e equa ion and he equa ions o he empo al e olu-
ion o ac i i y concen a ions in he h ee phases: wa e , suspended ma e and ac i e
bo om sedimen s. The ans e o adionuclides be ween wa e and he solid phases
has been desc ibed in e ms o kine ic ans e coe$cien s.

The suspended ma e sub-model has been es ed by compa ing obse ed and
compu ed suspended ma e dis ibu ions. Also, he suspended ma e #ux o he
No h Sea h ough he Do e S ai has been calcula ed. The compu ed #ux is in
ag eemen wi h p e ious es ima es.
The model has been applied o simula e he dispe sion o Cs and Pu
eleased om he nuclea uel ep ocessing plan a La Hague. In he case o Cs, he
esul s ob ained wi h an ea lie model, in which his adionuclide was conside ed o
emain in solu ion, ha e been imp o ed. This sugges s he impo ance o con-
amina ed sedimen s as a sou ce o adionuclides o he dissol ed phase. The model
gi es a ealis ic es ima ion o Pu ac i i y le els measu ed along he Channel in
wa e , suspended ma e and bo om sedimen s. Also, di!e en dis ibu ion maps ha e
been ob ained o conse a i e and non-conse a i e adionuclides, e ealing he
in#uence o suspended ma e on Cs and Pu dispe sion. Compu ed kB alues o
plu onium a e consis en wi h hose ecommended by IAEA (1985).
T ansi imes o adionuclides om La Hague o he cen al Do e S ai ha e also
been calcula ed using he c oss-co ela ion unc ion me hod. A ansi ime o
3 mon hs has been calcula ed o dissol ed adionuclides wi h a e age wind condi-
ions, in close ag eemen wi h p e ious calcula ions. The ansi ime inc eases o
4 mon hs i only ides a e conside ed. On he o he hand, a alue o 7 mon hs is
ob ained o eas e ly winds. In he case o a adionuclide wi h a high a$ni y o he
solid phases, like Pu, a ansi ime signi"can ly longe han ha o a dissol ed
adionuclide has been ob ained.
Acknowledgemen s
This wo k was pa ially suppo ed by ENRESA, EU con ac FI4PCT960046 and
Spanish CICYT con ac AMB97-1720CE.
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