Modelling he suspended ma e dynamics in a ma ine
en i onmen using a h ee dimensional coo dina e model:
applica ion o he eas e n I ish Sea
R. Pe iaan
~nez
*
Depa amen o Fı
ısica Aplicada 1, E.U. Ingenie ı
ıa Teecnica Ag ı
ıcola, C a U e a km 1, 41013 Se illa, Spain
Abs ac
A nume ical model o s udy he suspended ma e dynamics in he sea has been de eloped. The model
sol es he h ee dimensional hyd odynamic equa ions, ha a e w i en in no malized coo dina es so ha
e ical esolu ion is no educed in he shallowe egions. Wa e–cu en in e ac ion has also been included.
Simul aneously, he model sol es he suspended ma e equa ion, also w i en in no malized coo dina es,
ha includes ad ec ion, diffusion and se ling o pa icles. Deposi ion and e osion o he sedimen , ha a e
o mula ed using h eshold eloci ies, a e inco po a ed in o he sea bed bounda y condi ion o he sus-
pended ma e equa ion. A s anda d o mula o floccula ion has also been used. The model has been
applied o he eas e n I ish Sea. Compu ed and obse ed suspended ma e concen a ions ha e been
compa ed: bo h se o da a a e in good ag eemen . The model has also been es ed h ough he s udy o he
dispe sion o adionuclides eleased om a nuclea uel ep ocessing plan . Sensi i i y s udies ha e been
ca ied ou .
Keywo ds: Tides; Sedimen s; E osion; Deposi ion; Wind wa es; Wa e quali y
1. In oduc ion
Resea ch o suspended sedimen s in idal egimes has usually been ocused on ne a es o scou
o acc e ion. Howe e , in ecen yea s he e has been an inc easing in e es in modelling sus-
pended ma e since his is essen ial o wa e quali y models. Fi s , when sedimen is s i ed up
*
Tel.: +34-95-4233669; ax: +34-95-4232644.
E-mail add ess: [email p o ec ed] (R. Pe i
aa~
nnez).
nu ien s, ace me als and o ganic con aminan s a e eleased in o he wa e column. In
u n, as suspended sedimen se les ou he dissol ed chemicals may be sca enged. Secondly, since
he ligh in ensi y a dep h depends in e sely on suspended sedimen load in he wa e column
abo e, suspended ma e impac s on p ima y p oduc i i y [1]. Thus, ma hema ical models ha e
been de eloped o simula e he suspended ma e dis ibu ions in diffe en aqua ic en i on-
men s and unde diffe en app oaches. Howe e , al hough he applica ions o sedimen anspo
models a e wide sp ead, wo k on hei de elopmen is ela i ely sca ce. One eason o his lack o
models is ha many o he a iables associa ed wi h sedimen anspo a e no well de e mined
[2].
Ab il and Ga c
ııa-Le
oon [3] de eloped a wo dimensional, dep h a e aged, model o desc ibe he
basic aspec s o suspended ma e dynamics in he sea o e la ge ime scales. Thus, he model was
o mula ed in e ms o esidual (a e aged) wa e ci cula ion. The same app oach, bu using a
h ee dimensional model, was used [4] o s udy suspended sedimen s in he No h Sea. Wo ks in
[2] and [5] s udied he sho scale (bo h spa ial and empo al) aspec s. These models sol e he
dep h-a e aged ad ec ion–diffusion equa ion wi h he deposi ion and esuspension e ms, bo h
depending on he ins an aneous wa e s a e. Thus, he models equi e he simul aneous solu ion o
he hyd odynamic equa ions unde idal o cing. Bo h models we e applied o s udy he sus-
pended ma e dis ibu ion and he sedimen a ion p ocesses in es ua ine en i onmen s. A simila
app oach was adop ed [6], bu using a h ee dimensional model, o s udy a small ha bou sil a-
ion p oblem. Hol and James [7] s udied, using a 3D ba oclinic model, he dis ibu ion o sus-
pended ma e pa icles in oduced om se e al indi idual coas al sou ces in he sou he n No h
Sea.
By con en ion, pa icula e ma e in suspension is defined as he ma e ial ha is e ained on a
0.4–0.5 lm po e size fil e . Smalle ma e ial is conside ed o be dissol ed. Muddy sedimen s
consis s o clays wi h some a iable sil con en and pa icle diame e is [8] <62.5 lm. La ge
pa icles such as sands se le much mo e apidly ou o suspension in wa e han mud pa icles and
bed load anspo is he mos impo an mechanism in mo ing his coa se sedimen s [1,8].
Usually, only pa icles wi h a diame e <62.5 lm a e conside ed when modelling suspended
ma e dynamics [2,3,5,6,9,10]. Indeed, i has been poin ed ou [11] ha o all p ac ical pu poses
mud can be ega ded as synonymous o suspended ma e . Also, con aminan s ha e li le affini y
o coa se ma e ials and, on he o he hand, hey ha e li le influence in ligh in ensi y h ough he
wa e column since hey a e mainly anspo ed as bed load. Thus, he dynamics o muddy
sedimen s is much mo e in e es ing o wa e quali y s udies.
The objec i e o his pape is o p esen a h ee dimensional model ha can be applied o s udy
he suspended ma e dis ibu ion in a la ge ma ine en i onmen . In e es will ocus on he basic
aspec s o suspended ma e dynamics; aspec s ha ha e o be conside ed when de eloping a
wa e quali y model. The model sol es he h ee dimensional hyd odynamic equa ions, which a e
w i en in no malized coo dina es so ha e ical esolu ion is no educed in he shallowe
a eas, and, simul aneously, he suspended ma e equa ion is sol ed oo. This equa ion, also
w i en in no malized coo dina es, includes ad ec ion–diffusion p ocesses, se ling, deposi ion and
e osion o he sedimen s. Only muddy sedimen s a e conside ed in he model. The enhancemen in
bed s ess due o wa e–cu en in e ac ion may be essen ial o suspended sedimen anspo , and
his is pa icula ly impo an du ing majo wind e en s (when wa e heigh s a e la ge and swell
is significan ). Thus, a wa e–cu en in e ac ion model [12] has been included in he suspended
ma e anspo model. The model has been applied o simula e he suspended ma e dis i-
bu ion and he sedimen a ion a es in he eas e n I ish Sea. A nuclea uel ep ocessing plan a
Sellafield (see Fig. 1) eleases adionuclides o he sea. Some adionuclides, as o ins ance Pu and
Am, ha e a la ge affini y o be fixed o he solid phase (suspended ma e and bo om sedimen s).
Thus, he in o ma ion p o ided by his model is essen ial i we a e in e es ed, o ins ance, in
s udying he dispe sion o such pollu an s. Indeed, his suspended ma e model has been applied
o simula e he dispe sion o 239;240Pu. The compa ison be ween obse ed and compu ed plu o-
nium le els in wa e and suspended ma e p o ides an ex a alida ion o he suspended ma e
model.
The model equa ions a e p esen ed in Sec ion 2. A e , esul s a e p esen ed and discussed.
Some sensi i i y s udies ha e also been ca ied ou .
Fig. 1. Map o he compu a ional domain. The s a is Sellafield nuclea uel ep ocessing plan and ci cles a e he
poin s whe e suspended ma e concen a ions we e measu ed (see Sec ion 3.2). Each uni in he xand yaxis is 5000 m
(g id elemen numbe ). Con ou s ep esen he dis ibu ion in % o pa icles wi h a diame e <62.5 lm in he op
sedimen laye o he eas e n I ish Sea. A and B gi e he posi ions o compa men s (16, 20) and (10, 12), espec i ely.
2. The model
The ma ine a ea unde s udy is ep esen ed by a g id con aining a ce ain numbe o g id cells
o compa men s. The g id has uni o m spacing in he ho izon al, Dxand Dy, and spacing in he
e ical di ec ion is D , as will be shown below. Each compa men con ains a ce ain concen-
a ion mo suspended ma e in g=m3.
2.1. Hyd odynamics
The h ee dimensional hyd odynamic equa ions a e w i en using no malized coo dina es in
he e ical. This way a cons an numbe o g id boxes is used in he e ical a each ho izon al
g id poin and esolu ion is no educed in he shallowe a eas. The ans o ma ion o coo -
dina es is [13]
¼zþ
hþ ;ð1Þ
whe e his he undis u bed dep h o wa e , is he sea su ace displacemen om he mean le el
due o idal oscilla ions and zcoo dina e is measu ed om he mean sea le el o he bo om. Thus,
he hyd odynamic equa ions a e ans o med om he in e al  6z6hin o he cons an in-
e al 0 6 61. The o m o he equa ions in no malized coo dina es has been gi en p e iously
[13–15] and will no be epea ed he e. The bounda y condi ions applied a he sea su ace a e:
qNou
o

¼0
¼ðhþ ÞFs;ð2Þ
qNo
o

¼0
¼ðhþ ÞGs;ð3Þ
whe e Fsand Gsdeno e he componen s o he wind s ess ac ing on he sea su ace along he
xand ydi ec ions, Nis eddy iscosi y and qis he wa e densi y. Simila ly, a he sea bed
qNou
o

¼1
¼ðhþ ÞFb;ð4Þ
qNo
o

¼1
¼ðhþ ÞGb;ð5Þ
whe e Fband Gba e he wo componen s o he bed s ess.
A flow dependen eddy iscosi y, N, has been used in he model. This o mula ion has been
used p e iously and has gi en good esul s o idal flow s udies [16–18]
N¼CNffiffiffiffiffiffiffiffiffiffiffiffiffiffi

uu2þ
2
ph;ð6Þ
whe e CN¼0:0025 is a dimensionless expe imen ally measu ed coefficien and 
uu and 
a e dep h
mean cu en s along he xand yaxis, espec i ely. Eddy iscosi y has been aken cons an in he
e ical. This app oxima ion has also been used p e iously [17,19].
2.2. Wa e–cu en in e ac ion model
The effec o enhanced bed u bulence due o wind wa es influences he idal cu en by an
inc ease in he cu en ic ion ac o , c, hus p oducing an inc ease in he bed s ess componen s
Fband Gb. These a e w i en using he ollowing linea laws [14,15]:
Fb¼1
2 cquðbÞ;ð7Þ
Gb¼1
2 cq ðbÞ;ð8Þ
whe e uðbÞand ðbÞa e he nea bed cu en componen s, usually specified 1 m abo e he bed [12].
I is also usual o define a ic ion coefficien as k ¼ c=2. Al hough a quad a ic law o bo om
ic ion is now mo e ex ended han a linea o mula ion, he linea law has been used since a as e
con e gence o he equa ions is ob ained [15]. Also, he e a e no app eciable diffe ences i he
model is calib a ed using a quad a ic law ins ead o he linea one [15].
Following [12], he o al bed shea s ess, s , based upon a cu en shea s ess, sc, and a wa e
shea s ess, sw,is
s ¼scþswð9Þ
wi h
sw¼1
2 wqU2
w;ð10Þ
whe e wis he wa e ic ion ac o and Uwis he maximum wa e o bi al eloci y
Uw¼aww
sinhðkhÞð11Þ
wi h awwa e ampli ude, wwa e angula speed and kwa e numbe de e mined om he dis-
pe sion ela ion
w2
g¼k anhðkhÞ;ð12Þ
whe e gis he accele a ion due o g a i y. I is assumed [12] ha he cu en does no influence he
wa e field ( his is a consis en assump ion wi h he me hod used in his wo k in which he model
is un wi h he wa e field supplied ex e nally, and hus, he e is no dynamic eedback om he
hyd odynamic model).
The calcula ion o an effec i e d ag coefficien c aking in o accoun wa e effec s is ca ied ou
as ollows. The wa e ic ion eloci y is
Uw¼ffiffiffiffiffiffiffiffiffiffi
sw=q
pð13Þ
wi h swgi en om Eq. (10). A ¼0, an ini ial c, no accoun ing o wa es, is compu ed om
c¼K
lnð30z Þ=kbc

2
;ð14Þ

whe e K(0.4) is he on Ka man’s cons an , kbc is aken as he Niku adse oughness kb
(kb¼30z0;z0being he oughness leng h) and z is a e e ence le el abo e he bed usually aken
[12] as 1 m.
Once cis de e mined, he cu en ic ion eloci y is
Uc¼ffiffiffiffiffiffiffiffiffi
sc=q
pð15Þ
wi h sc he ec o sum o Fband Gb om Eqs. (7) and (8). The combined ic ion eloci y Ucw o
wa es and cu en s is
Ucw ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
U2
cþU2
w
q:ð16Þ
The appa en bo om oughness kbc el by he cu en due o he p esence o wa es is gi en by
kbc ¼kbC1
UcwAb
Uwkb

b
ð17Þ
wi h
b¼1Uc
Ucw
;ð18Þ
C1¼24:0ð19Þ
and a wa e nea bo om excu sion ampli ude Ab¼Uw=w. This alue o kbc is used a he nex ime
s ep o de e mine c om Eq. (14) and hence he bed s ess in he h ee dimensional hyd odynamic
model om Eqs. (7) and (8). A mo e de ailed desc ip ion o he wa e–cu en in e ac ion model
can be seen in [12].
2.3. Suspended ma e equa ions
The h ee dimensional suspended ma e equa ion has been ob ained by ans o ming he
equa ion p oposed by Nicholson and O’Conno [6] in o coo dina es. Such equa ion includes
ad ec i e–diffusi e anspo plus e ical all (se ling) o suspended pa icles
om
o þuom
oxþ om
oyþwom
o
¼o
oxKh
om
ox

þo
oyKh
om
oy

þ1
ðhþ Þ2
o
o K
om
o

1
hþ
oðwsmÞ
o ;
ð20Þ
whe e mis he suspended ma e concen a ion in g=m3,wis he e ical wa e eloci y along he
axis, uand a e wa e eloci ies along he xand yaxes, Khand K a e he ho izon al and e ical
diffusion coefficien s, espec i ely, and wsis he se ling eloci y o suspended pa icles.
The e ical diffusion coefficien can be w i en as a unc ion o he eddy iscosi y [20]
K ¼N;ð21Þ
whe e he non-dimensional numbe  anges [21] om 0.1 o 0.5.
I is assumed ha he e is no flux o pa icles h ough he sea su ace. Deposi ion and e osion o
he sedimen a e inco po a ed in o he sea bed bounda y condi ion [6]
1
hþ K
om
o

¼1
ðwsmÞ ¼1¼E qMwsðbÞmðbÞ1
q
qcd :ð22Þ
The fi s e m o he igh membe o he equa ion ep esen s e osion: Eis he e osion cons an
o e odabili y ha also ac s as a scaling ac o , Mis some powe o he wa e eloci y, ypically
[22] in he ange 2–5, and gi es he ac ion o pa icles wi h a diame e <62.5 lm in he sedi-
men . This way, he o mula de i ed by Fukuda and Lick [23] and La elle e al. [24] 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 a diame e <62.5 lm can be inco po a ed as suspended ma e in o he wa e
column, as has been discussed abo e. I is conside ed ha e osion occu s only when he nea bed
cu en magni ude, q¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2ðbÞþ 2ðbÞ
p, is la ge han an e osion h eshold eloci y qce. O he wise
he e osion e m is se o ze o. The second e m ep esen s deposi ion o pa icles on he sea bed,
ha has been based on he concep by Teisson [25] and also used by Cla ke [2]. No e ha ðbÞ
means ha he co esponding magni ude is e alua ed a he e e ence le el z ¼1 m abo e he
bed. qcd is he deposi ion h eshold, hus deposi ion occu s only i q<qcd; o he wise his e m is
se o ze o.
Small sedimen pa icles end o join oge he o o m la ge uni s called flocs. Thus, hese
pa icles a e e med cohesi e sedimen s [8]. Floccula ion affec s he se ling eloci y in such a way
ha i inc eases wi h concen a ion a low concen a ions, hen a ains a maximum alue and
he ea e dec eases due o hinde ed se ling. A s anda d o mula used o ep esen he effec o
floccula ion is [2,6,26–29]
ws¼amb;ð23Þ
whe e aand bha e o be ob ained om measu emen s o om model calib a ion. I mus be
no ed ha hinde ed se ling occu s a suspended ma e concen a ions o he o de o [28] 103
ppm, hus Eq. (23) is alid when concen a ions a e smalle han his alue. Since concen a ions
in he I ish Sea a e o he o de o 1 ppm (see below) hinde ed se ling effec is no included in he
model. Indeed, concen a ions o he o de o 103ppm a e no ound in he sea [28].
A sou ce e m mus be included o he suspended ma e equa ion in hose g id cells loca ed
along he coas line. This e m ep esen s he inpu o pa icles om unoff o con inen al wa e s
[3] and can be w i en as
cIi;j;ð24Þ
whe e c ep esen s he mass o suspended load pe con inen al wa e olume uni and Ii;jis he
o al olume o con inen al wa e ha en e s compa men i;j.Ii;jwill be diffe en om ze o when
he compa men is si ua ed along he coas line.
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 ime s ep, bu also gi es in o ma ion o he
sedimen a ion p ocesses ha ake place in he a ea unde s udy. Thus, he ne sedimen a ion a e,
RS, is ob ained as he diffe ence be ween he deposi ion and e osion e ms
RS¼wsðbÞmðbÞ1
q
qcd E qM:ð25Þ
2.4. Nume ical solu ion
The hyd odynamic equa ions a e sol ed using a fini e diffe ence explici scheme, al hough he
Saul’e me hod [29] is applied o he e ical diffusion e m o e ain s abili y [30]. Some bounda y
condi ions mus also be gi en. A closed bounda ies he no mal componen o he cu en and he
flux o suspended pa icles a e se o ze o. Along open bounda ies, ampli ude and phase o he sea
su ace ele a ion a e specified om obse a ions. Since ou objec i e consis s o ep oducing he
basic ea u es o suspended sedimen dynamics in he sys em, only he main idal cons i uen , M2,
has been used. O cou se, be e esul s would be ob ained i o he cons i uen s (a leas N2and S2)
a e included, since hey will enhance e osion. Howe e , as will be shown below, he basic aspec s
o suspended ma e dis ibu ion (and also o plu onium dispe sion) can be ob ained al hough
only he M2 ide is included. Mo eo e , as will also be shown, i seems ha suspended ma e
concen a ions a e no domina ed by e osion e en s. Thus, i is no expec ed ha he inc ease in
bed s ess p oduced by hese o he cons i uen s p oduce a significan change in e osion and in
suspended ma e concen a ions.
The su ace cu en componen ha is no mal o he open bounda y is ob ained om a a-
dia ion condi ion [21,31]. The open bounda y condi ion desc ibed in [15] is applied o he sus-
pended ma e equa ion.
The ad ec ion and diffusion e ms in he suspended ma e equa ion a e sol ed using second-
o de accu acy explici schemes [21] and he Saul’e me hod is again applied o he e ical di -
usion e m.
A FORTRAN code has been de eloped o sol e he equa ions in ol ed in ou model. Such
code was implemen ed on a HP X-Class compu e .
3. Resul s and discussion
3.1. Model applica ion
The compu a ional domain, co e ing he eas e n I ish Sea, is p esen ed in Fig. 1. The model has
a ho izon al esolu ion Dx¼Dy¼5000 m and ime s ep is fixed as D ¼60 s. Ten laye s a e
conside ed in he e ical, hus D ¼0:1. All s abili y condi ions [21] a e sa isfied wi h hese se-
lec ions.
Wa e dep hs a e in oduced om ba hyme ic maps and ange om 55 m in he wes o a
shallowe egion a ound he B i ish coas . The ac ion o pa icles wi h a diame e <62.5 lmin
he sedimen , , has been specified om obse a ions [3,32] and he dis ibu ion is also p esen ed
in Fig. 1. I can be seen ha he e is a mud bank ha lies along he B i ish coas and a smalle one
loca ed be ween Anglesey and he Isle o Man. Sea su ace ele a ions and phases along he open
bounda y ha e also been ob ained om obse a ions [33].
The mean alue 0.3 has been aken o in Eq. (4). The ho izon al diffusion coefficien has been
fixed as Kh¼500 m2=s since esul s in ag eemen wi h obse a ions a e ob ained wi h his alue.
I has been sugges ed [34] ha o he I ish Sea 500 <Kh<900 m2=s and, also, his alue has been
success ully used in p e ious modelling wo k [15]. Indeed, he ad ec ion–diffusion dispe sion
equa ion has been p e iously calib a ed, which consis s o selec ing he op imum diffusion coe -
ficien s and bounda y condi ions, h ough he nume ical s udy o he dispe sion o 137Cs in he
eas e n I ish Sea [15]. In such pape , obse ed and compu ed dis ibu ions o dissol ed 137Cs we e
compa ed, p o iding a wide alida ion o he dispe sion model. The op imum selec ions ob ained
in [15] a e now used in his wo k o simula e he suspended ma e dynamics.
One o he main difficul ies in sedimen anspo modelling is he me hod o ob aining he
e osion and deposi ion h esholds and he e odabili y cons an . Thus, hey a e selec ed, by ial
and e o , in such a way ha hey p oduce he bes fi o model esul s o obse a ions, al hough
pa ame e s mus be physically ealis ic.
A alue o 0.18 m/s has been used o he deposi ion h eshold eloci y [5,28] and a ypical alue
[8,35] o 0.21 m/s has been aken o he e osion h eshold eloci y. Indeed, i has al eady been
poin ed ou [2] 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 when deposi ion ends and e osion begins. 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 effec
on e osion o deposi ion. Thus, usually [2] qcd <qce. On he o he hand, a e some model uns, a
alue o 2:7104gm
11=2s5=2was selec ed o he e odabili y cons an and i was aken
M¼3:5.
In Eq. (23), i was aken a¼1:7106and b¼1:6i mis gi en g=m3and wsin m/s. Since
suspended ma e concen a ions in he I ish Sea a e o he o de o 1 g=m3, se ling eloci ies o
he o de o 106m/s a e ob ained, which is he o de o magni ude ha can be ound [22,36] o
he se ling eloci y o cohesi e sedimen s. I can be ound in li e a u e [27,28] ha b anges
be ween 0.5 and 2.0. A alue o 1.6 has also been ob ained [26] and was used in p e ious mod-
elling wo k [5]. I can be ound in li e a u e ha a anges om 103 o 109[2,26].
c(Eq. (24)) was fixed, a e a calib a ion exe cise, as 25 g=m3. Al hough he e can be seasonal
a ia ions in his pa ame e , i has been aken cons an . Thus, he model gi es an es ima ion o he
a e age suspended ma e concen a ion o e he sea. The inpu o con inen al wa e s, Ii;j, was
ob ained om [37], also p esen ed in [3].
3.2. Suspended ma e dis ibu ion in he eas e n I ish Sea
The hyd odynamic pa o he model was es ed by compa ing obse ed and compu ed alues
o ide ampli udes and phases and semi-majo axis magni ude and di ec ion o he M2cu en
ellipse a diffe en dep hs and loca ions. A e a calib a ion p ocess, he ic ion coefficien was
ini ially fixed as k ¼0:011 (wi hou wa e–cu en in e ac ion) o he whole model domain. The
diffe ence be ween compu ed and obse ed idal ampli udes is always <10%, only in one poin is
17.4% (compa isons ha e been made o 12 poin s). In he case o idal phases, absolu e alues o
he diffe ences be ween obse ed and compu ed phases ange om 0° o 27°, being he mean alue
10.5°. The diffe ence be ween compu ed and obse ed semi-majo axis magni ude o he M2
cu en ellipse anges om 1.5% o 45%. Only in h ee poin s e o s a e abo e 25% (12 poin s used
o compa ison). The absolu e alue o he diffe ence be ween obse ed and compu ed o ien a ion
o he axis anges om 0.1° o 30.5°, being he mean alue 7.6°. De ails can be seen in [15] and will
no be epea ed he e. Fo he M2 ide, s ong ec ilinea flow wi h cu en ellipses aligned in a
wes –eas di ec ion occu s in he no he n and sou he n pa s o he eas e n I ish Sea, sepa a ed
by an a ea o significan ly weake , nea ci cula , ellipses o he eas o he Isle o Man. Wi h
The model esponse when he se ling eloci y is changed (inc easing and dec easing ain Eq.
(23) by a ac o 3) is shown in Fig. 9(c). I can be seen ha an inc ease in aleads o lowe sus-
pended ma e concen a ions since se ling is enhanced. Al e na i ely, highe concen a ions a e
ob ained when ais dec eased. Again, a ia ions in aaffec s mainly he egions loca ed close o he
coas , whe e suspended ma e concen a ions a e highe (see Eq. (23)).
Finally, i has been ound ha essen ially he same esul s a e ob ained i an e osion h eshold
eloci y is no used. Indeed, i has been ecen ly poin ed ou [22] ha he s ipula ion o a minimum
h eshold eloci y below which no e osion occu s o en has li le effec in idal condi ions whe e
eloci ies exceed 0.5 m/s, as is he case [15]. On he o he hand, oo low suspended ma e con-
cen a ions a e ob ained i a deposi ion h eshold is no used. Thus, deposi ion h eshold mus be
conside ed in he deposi ion e m.
4. Conclusions
A dynamic model o s udy he suspended ma e dis ibu ion in he eas e n I ish Sea has been
de eloped. The model sol es he h ee dimensional hyd odynamic equa ions, which a e w i en in
Fig. 9. (a) Measu ed and compu ed suspended ma e p ofiles (ppm) ollowing he poin s o [41], shown in Fig. 1, in
su ace wa e s. ‘‘compu ed’’ a e he model esul s when pa ame e s p esen ed in Sec ion 3.1 a e used. ‘‘A’’ a e esul s
when Eis inc eased by 3 and ‘‘B’’ a e model esul s when Eis dec eased by a ac o 3. (b) Same as (a), ‘‘A’’ and ‘‘B’’ a e
esul s when cis doubled and hal ed, espec i ely. Same as (a), ‘‘A’’ and ‘‘B’’ a e esul s when ais inc eased and
dec eased, espec i ely, by a ac o 3.

no malized coo dina es, wi h a flow dependen o mula ion o he eddy iscosi y. Simul a-
neously, he model sol es he equa ion ha go e ns he suspended ma e dynamics, which is also
w i en in no malized coo dina es. The suspended ma e equa ion includes ad ec ion, diffusion
and se ling o pa icles. Deposi ion and e osion a e included in o he sea bed bounda y condi ion
o he equa ion and a e o mula ed using h eshold eloci ies. A s anda d o mula o ep esen
floccula ion has also been used. The model includes a sou ce e m o ake in o accoun he inpu
o pa icles om unoff o con inen al wa e s.
The model has shown ha suspended pa icles a e well mixed e ically in he eas e n I ish Sea
and ha suspended ma e concen a ions a e no domina ed by e osion e en s. Indeed, small
sedimen a ion a es ha e been ob ained, showing ha no majo e osion o deposi ion is aking
place a p esen ime. Measu ed and compu ed suspended ma e concen a ions in he sea ha e
also been compa ed. Model esul s a e in ag eemen wi h obse a ions, hus, i seems ha he
model gi es a ealis ic ep esen a ion o he suspended ma e dis ibu ion in he eas e n I ish Sea.
I has been ound ha wa e–cu en in e ac ion affec s he e osion a e o he muddy a ea
loca ed be ween Anglesey and he Isle o Man, bu e osion is no significan ly al e ed in he es o
he sea. Howe e , he e is ad ec ion o suspended pa icles due o he wind induced cu en .
The suspended ma e model has been used o simula e he dispe sion o 239;240Pu eleased o he
sea om Sellafield nuclea uel ep ocessing plan . I has been ound ha he e a e significan
diffe ences be ween he su ace and bo om Pu concen a ions in suspended ma e . Thus, he use
o a 3D model is ele an o wa e quali y s udies, al hough he e a e no impo an diffe ences
be ween he su ace and bo om suspended ma e concen a ions.
Acknowledgemen s
Wo k pa ially suppo ed by EU Con ac FI4PCT960046, Spanish CICYT Con ac AMB97-
1720-CE and ENRESA.
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