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Internal Wave Turbulence Near a Texel Beach
Hans van H aren1*, Louis G ostiaux2, M artin Laan1, M artijn van H aren3, Eva van H aren3, Loes J. A.
G erringa1
1 Royal Netherlands Institute for Sea Research, Den Burg, The Netherlands, 2CNRS/Grenoble-INP/UJF-Grenoble 1, Laboratoire des Ecoulements Géophysiques et
Industriels, Grenoble, France, 30SG de Hogeberg, Den Burg, The Netherlands
A bstract
A s u m m e r b a t h e r e n te r in g a c alm se a from t h e b e a c h m ay s e n s e a lte rn a tin g w a r m a n d cold w ater. This c an b e felt w h e n
m o vin g forw ard into t h e se a (Vertically h o m o g e n e o u s ' a n d 'horizontally different'), b u t also w h e n s t a n d in g still b e t w e e n
o n e 's fe et a n d b o d y ('vertically different'). On a calm su m m e r - d a y , a n array of high-precision se n so rs has m e a s u r e d fast
t e m p e r a t u r e - c h a n g e s u p to 1°C n e a r a Texel-island (NL) be ac h. The m e a s u r e m e n t s s h o w t h a t s e n s e d variations are In fact
Internal waves, fro nts a n d tu rb u le n c e , s u p p o r t e d in part by vertical sta b le stratification In d e n sity (te m p e ra tu re ). Such
m o tio n s are c o m m o n in t h e d e e p o c ea n , b u t ge nera lly n o t in shallow se a s w h e r e t u r b u l e n t mixing is e x p e c t e d stro n g
e n o u g h t o h o m o g e n i z e . T he internal b e a c h -w a v e s have a m p l i tu d e s te n - t i m e s larger t h a n t h o s e o f t h e small surface wind
waves. Q uantifying th e ir t u r b u l e n t mixing gives dlffuslvlty e s t im a te s of 10- 4 - 1 0 - 3 m 2 s - 1 , w hich a re larger t h a n fo u n d In
o p e n - o c e a n b u t sm aller t h a n w a v e breaking a b o v e d e e p slop ing to p o g r a p h y .
C itation : van Haren H, Gostiaux L, Laan M, van Haren M, van Haren E, et al. (2012) Internal Wave Turbulence Near a Texel Beach. PLoS ONE 7(3): e32535.
doi:10.1371/joumal.pone.0032535
Editor: Vanesa Magar, Plymouth University, United Kingdom
Received November 1, 2011; A ccepted January 31, 2012; Published March 5, 2012
C opyrigh t: © 2012 van Haren et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The authors have no funding or support to report.
C om peting Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected]
Introduction
am plitudes th a n surface w ind waves (SWW). D ensity stratification
ham p ers vertical tu rb u le n t exchange o f h eat a n d n utrients due to
its stability. C o u n tera ctin g destabilization occurs internally, as IW
m ay break, a n d even m ore energetically n e a r low er a n d u p p e r
b oundaries due to (tidal) c u rre n t friction at the b o tto m a n d
atm ospheric cooling a n d w ind shear stress a t the surface. F or the
southern N o rth Sea, winds, S W W -breakers a n d > 0 .4 m s 1 tidal
currents are com m only th o u g h t to m ix solar h e atin g from surface
to b o tto m y e ar-ro u n d [7], except for fresh-w ater outflows.
W e will show th a t IW can occur even at one o f the w indiest
spots o f the N etherlands, n e a r a b eac h o f T exel-island. T his is
w here norm ally S W W -breakers reside, except after a prolonged
p e rio d o f fine days for the entire region w ith strong insolation th at
is not m ixed aw ay by atm ospheric a n d tidal b o u n d a ry stresses. W e
quantify the ra te o f tu rb u le n t m ixing b y these ‘b e ac h -IW ’.
T h e presen t oceanographic view is th a t in shallow w aters o f only
a m etre deep, te m p e ra tu re (T) m ust be hom ogeneous by tu rb u len t
tidal a n d w ind m ixing. In contrast, w hen asked, Italian m others,
lazily ch attin g in w ater up to th eir w aist in sum m ertim e A driatic
Sea w hile overlooking th eir offspring, experience not a constant
w ater tem p e ra tu re b u t slowly alte rn a tin g w arm a n d cooler blobs o f
varying height [M argiotta, pers. com m .., 2011], N ow , this is an
a rea w here surface w ater tem p eratu res reach T w = 29"C , n e a r the
range o f n e u tra l h u m a n am b ien t skin-tem perature at w hich b o th
w arm a n d cold fibers are active. H u m a n th erm o cep tio n starts at
0 .5 - T C T -difference, from physiology experim ents o f small bodysurfaces a ro u n d 32"C [1-3], b u t b o d y cooling reduces local
th erm al sensitivity [4]. H ow ever, reg u lar b e ac h visitors in
countries like the N eth erlan d s (TW< 2 0 "C ) confirm : slow m inutelike T -variations can b e sensed, w h en seas are calm .
H e re w e investigate using high-resolution T -sensors w h eth er
bath ers in the N o rth Sea experience physical p h e n o m e n a like
‘fronts’ a n d ‘internal w aves’ a n d w h at tem p e ra tu re differences
th eir bodies sense u n d e r relatively cold conditions. Such physical
p h e n o m e n a co m m o n in the ocean interior have never been
quantified close to shore. T h e presen t study proofs suppositions
ab o u t shorew ard extent o f internal waves from historic observa­
tions in > 5 m w ater off Scripps a n d O ceanside piers in the Pacific
[5,6].
As seas (and oceans) are h e ated from above a n d w arm w ater is
less dense (“lighter”) th a n cold w ater, they a re generally stably
stratified in density. Fresh above salty w ater contributes also
positively to density stratification. A stratified sea supports m otions
in its interior th a t basically go unno ticed at the sea surface: internal
waves (IW) w hich p ro p a g ate m u ch slower b u t w ith m u ch larger
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M aterials a n d M ethods
N o specific perm its w ere req u ire d for the described field studies.
N o specific perm issions w ere re q u ire d to p erfo rm N IO Z
m easurem ents at T exel beach. T h e location is n o t privatelyow ned o r p ro tec te d in any way. T h e field studies did not involve
en d an g e red or p ro tec te d species.
A total o f 36 ‘N IO Z 4 ’ self-contained tem p e ra tu re (T) sensors
sam pling at 2 H z, w ith precision b e tte r th a n 0 .0 0 TCI [8], w ere
m o u n te d at 0.042 m vertical intervals o n a w ooden pole (Fig. 1).
T h e lowest sensor was 0.13 m from the bo tto m . T w o sensors
failed, including the lowest. T h e pole was fixed to the sandy,
slightly und u latin g a n d weakly sloping b o tto m using two concrete
slabs, w eighing ~ 4 0 kg each (in air). O n six selected days o f calm
w eath er a n d small SW W it was m o o red a t 53" 0 2 .9 4 4 'N , 04"
4 2 .8 0 0 'E (near T exel beach-pole 13), H = 0 .6 m a t low -w ater
1
March 2012 | Volume 7 | Issue 3 | e32535
Internal Wave Turbulence Near a Texel Beach
d
K z = 0 .1 2 8 d 2N .
(2)
Results
4—
1I
__________ J L
A
.
a
D u rin g the fortnight o f observations, w ater w arm ed steadily on
average. T h e short-scale p h e n o m e n a to be described here w ere
observed in all six records, although w ith som e variations in
intensity. W e analyze the longest observation p erio d o f 11 hours
on 30 J u n e 2010 (yearday 180). T h e pole was m o o red a ro u n d
sunrise, tim e o f LW +1 h. U ntil day 180.26 (06:30 U T C ; 08:30 LT)
hum idity was 100%, w ind speed | W | < 2 m s ’, air tem p e ra tu re
T a< T „ a n d in sea no T -differences w ere observed (Fig. 2). C loudcover rem a in e d high (60-100%) the entire day, w ith some
sunshine betw een days 180.3 a n d 180.4 w hen h um idity reach ed
a m in im u m o f 80%. A daily evap o ratio n sum o f 0.7 nin i is
calculated for these conditions [14], im plying a salting o f 0.02 PSLT
m . T o balance this density con trib u tio n one requires ~ 0 .D C o f
w arm ing; the observed te m p e ra tu re differences w ere m u ch larger.
Potentially stratification counteracting, fresh g ro u n d w ater leakage
is found little im p o rtan t, as it w ould generate free convection in the
overlying saltier sea w ater, hence com plete hom ogenizing.
T a,max= 22uC a ro u n d day 180.55, w hen the easterly w ind-speed
equaled 4—5 m s *. Such w inds could increase stratification in
concert w ith lateral density gradients, b u t variations as presen ted
below w ere also observed du rin g periods o f no w ind. Easterly
w inds c rea te d only small surface w aves n e a r the pole, as the beach
is exposed to the W est. SW W -height including swell was a bout
0.1 m (Fig. 2a, yellow bar) w ith 3-10 s periods.
T -observations in the sea (Fig. 2a) v aried b etw een 17.05 a n d
18.97"C (in satu rated to the right). In the b eginning o f deploym ent
w hen T a< T w, stratification was very w eak, alth o u g h the u p p e r
layer was still 0.03"C w arm er th a n near-b o tto m , a n d occasionally
even, ap p aren tly unstable (cool above w arm ). As soon as T a> T w,
w ell-stratified w ater passed T -sensors th a t w ere now all below
surface (at H W sea level is ab o u t 0.90 m above the highest sensor).
A ro u n d H W m ore th a n 1UC w a rm er w ater passed in different
ways: slowly varying w ith periods o f a few hours (Fig. 2a after day
180.265), w ith periods o f h a lf a n h o u r (180.30-180.38) a n d m ore
rapidly w ith changes every 6 0 -9 0 s (Fig. 2b,c): trains o f IW w ith
vertical am plitudes varying b etw een 0.2 a n d > 1 .0 m . T -variations
thus occupied a substantial p a rt o f the w ater colum n. Such 0 .5 D C tem p e ra tu re differences w ere sensed b y team m em bers,
regularly sw im m ing o r standing in the sea n e a r the pole w ithout
disturbing the m easurem ents (Fig. lb).
H e atin g from the atm o sp h ere does not directly force IW , as
stable w arm w ater initially spreads like a p ancake over colder
w ater. IW -am plitudes are m u ch larg er th a n S W W ’s a n d their
periods 0 (1 0 0 -1 0 0 0 s) are m u ch longer th a n 10 s.
D etails show th a t irregular internal m otions also occur th a t can
have periods o f 10-30 s (Fig. 2b,c). T hese can n o t b e in te rp rete d as
freely p ro p a g atin g IW , as local stratification has a smallest
b uoyancy p e rio d o f T N~ 6 0 s w h en calculated in extrem ely thin
layers < 0 .1 m , even tho u g h using the conservative densityte m p e ra tu re relationship. Instead, these short-period m otions
represent tu rb u len t overturns, e.g., day 180.3346 (Fig. 2b) a n d
days 180.2876, 180.2912 (Fig. 2c), follow ing different (IW-)
currents above a n d below shearing a n interface a n d rolling it
up. T hese overturns have periodicities betw een IW a n d SW W
[15]. S hear m agnitude (|S|) is not m easu red here, b u t
extrap o latin g from historic central N o rth Sea observations [16],
we can expect |S |~ N ~ O ( 1 0 -1 s- 1 ).
1
.M
Figure 1. Instrum ent pole (up per sensor 1.60 m abo ve the
b o tto m ) near Texel beach w ith shorew ard small surface w ave
breakers (thin w h ite line close to th e beach), a. A long-beach view,
b. Beach-view with differential w ater te m p e ra tu re sensing. The p h o to s
are taken an ho u r b efore low-water.
doi:10.1371/jo u rn al.pone.0032535.g001
(LW), d u rin g periods varying from h a lf a n h o u r to nearly a tidal
p erio d w ithin a span o f 14 days in J u n e /J u ly 2010. A t T exel beach
we do not n e ed specific perm its for w ater te m p e ra tu re m easure­
m ents. T his tim e-span covered a n atm ospheric high-pressure
system over the region a n d calm , w arm w eather. D istance to shore
(high-w ater, H W , m ark) was approxim ately 100 m . P redicted tidal
range is 1 .8 ± 0 .2 m , w hich includes spring-neap variation.
M eteorological d a ta are available from a irp o rt D e n H eld er
(15 km southw ard). SW W am plitudes a n d periods are estim ated
from air-w ater surface passing the T -sensors.
T h e T -d a ta are used as a conservative estim ate for density (p)
variations, using standard relation, Sp = —aST, a = 0.23 kg m 3 "Ci 1
denoting the therm al expansion coefficient u n d e r local conditions.
L acking salinity (S) d a ta it is assum ed th a t only tem perature
contributes to Sp. As will be show n in Section 3, ev aporation (salting
the surface) contributes less to density th a n heating. D ifferential
horizontal advection will reinforce solar heating stratification,
because in sum m er the fresher inland tidal-flat W ad d e n Sea,
b o rd e rin g T exel o n its eastern side, is w arm er th a n the saltier N o rth
Sea [9], H ence, the above density-tem perature relationship is a
conservative one.
V ertical tu rb u le n t eddy diffusivity K z a n d tu rb u le n t kinetic
energy dissipation rate s are estim ated b y calculating ‘o v ertu rn in g ’
scales using T -d ata. T hese scales are o b tain e d after reordering
every tim e-step potential density (tem perature) profile, w hich m ay
c ontain inversions, into a stable m onotonie profile w ithout
inversions [10,11], A fter co m p arin g raw a n d re o rd e re d profiles,
displacem ents (d) are calculated necessary for g enerating the stable
profile. A certain threshold applies to disregard a p p are n t
displacem ents associated w ith instrum ental noise. T his is very
low for N IO Z -th ern iisto r d ata, < 5 x l 0 - 4 "C [8], T h en ,
g = 0 .6 4 d 2N 3,
(1)
w here N denotes the b uoyancy frequency c o m p u ted from the
re o rd e re d profile a n d the constant follows from em pirically
relating the overtu rn in g scale w ith the O zm idov scale L o = 0.8d
[12]. LTsing K z = T s N - 2 a n d a m ixing efficiency for conversion o f
kinetic into poten tial energy o f T = 0.2 [13], we find,
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Internal Wave Turbulence Near a Texel Beach
180.2
V Tw 180.3
HW
180.4
180.5
180.6
I
1000 s
9 :36
180.334
12 (hh:mm UTC) 14:24
1 8 0 .3 3 5
7"
^
180 .3 3 6
w
_q
E
17.2
1 8 0 .2 8 8
18 0.2 89
1 8 0 .2 9
180.291
1 8 0 .2 9 2
(y e a r d a y )
Figure 2. A lm ost one tidal period overview o f detailed tem p e ra tu re (T) variations near Texel beach in ea rly sum m er. The vertical scale
is 1.75 m with reference to th e b o tto m . For display purposes, th e colour-scale d o es n ot com pletely cover th e observed w ater te m p e ra tu re range of
[1 7 .0 5 ,18.97]°C. a. The small red bars indicate zoom s in b., c. and th e large o n e indicates th e period o f Figure 3. The vertical red-in-w hite line indicates
w hen Ta = Tw using u p p e r therm istor in w ater and atm o sp h eric d a ta from Den Flelder-airport. The black dash ed curves indicate th e pred icted tidal
sea-level h eig h t variation (sensors in air above it) an d th e yellow bar on th e left sp read of surface w ind w ave height, estim ated from th e w ater surface
passing T-sensors. Time (UTC) is 0.33 hours b efore local SolarTime. b. Zoom of a front an d trailing 80 s period IW and sh o rter period IW -turbulence
m otions, c. Zoom o f high-frequency (60 s period) internal w aves an d sh o rter scale overturning.
doi:10.1371/jo u rn al.pone.0032535.g002
A transition betw een w arm a n d cold w ater passes, w hich is m ore
th a n 1.2 m in height (Fig. 2b). It m im ics a frontal passage, like in the
atm osphere. N e ar the b o tto m it seems to b e unstable (Fig. 2b, day
180.3345: w ater n e a r the b o tto m w arm er th a n halfw ay up) a n d m ay
thus break thereby generating turbulence. T h e “w aves” riding the
near-b o tto m stratification are not p ro p ag atin g IW , b u t have SW W am plitudes a n d periods: p u m p in g up- a n d dow n the w ater colum n.
T h e larger am plitude a n d -period front-trailing waves include
asym m etric turbulence-like m otions.
A train o f finescale IW w ith tu rb u le n t m ixing cores a n d
o v ertu rn in g (Fig. 2c) shows every m inute T -v ariatio n o f 0.5"C
across ~ 0 .5 m in the vertical.
W e quantified this tu rb u le n t m ixing (Fig. 3). U ntil day 180.265
(Fig. 3a; red-in-w hite line indicates in d ep e n d en t estim ate T w = T a)
the near-hom ogeneous layer (Fig. 3a,b) is weakly stable w ith
occasional overturns (Fig. 3c). T h is m ixing is likely driven
follow ing nighttim e air-sea interaction. It provides vertical average
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< K Z> = 1—3 x l 0 - 5 m~ s“ 1 (Fig. 3d). T h e associated h eat filix (not
shown) a n d turb u len ce dissipation ra te (Fig. 3e) a re n o t very large
(s < 1 0 8 W kg *) because stratification is so weak.
T ran sitio n (d a y > 180.265; T a> T w) is a b ru p t from w eak to
strong stratification. A fter a n o v ertu rn in g front, turbulence
p a ram ete rs d ro p one-tw o orders o f m agnitude, even tho u g h T variatio n is initially a few tenths o f degrees. H ow ever, periods
w hen turbulence a pproaches m olecular diffusion/noise level
values (10- 7 < K z< 10- 6 m~ s- 1 ; s < 1 0 - 9 W kg- 1 ) are ra re a n d
th ro u g h the entire range small spots o f < K Z> ~ 1 0 5 m~ s *;
s —10- 8 W kg-1 are observed. T hese spots are associated w ith
short-period w eak IW -overturning. IW -am plitudes, stratification
a n d turbulence gradually intensify until day 180.31. H ighest values
(Kz = IO-3 m 2 s- 1 ; s = IO-5 W kg- 1 ) are in the u p p e r h a lf o f the
observation z-range.
A fter day 180.31, w h en larger-scale IW m oves u p a n d cooler
b o tto m w ater m ove in, turbulence becom es w eaker (in Fig. 3) until
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Internal Wave Turbulence Near a Texel Beach
18.2
18 T (°C )
17.8
-Q
<U
E
17.6
N
117.4
117.2
1-1
-1.5
log(N) (s'1)
.Û
ro
E
2
N
-2.5
.1
0.5
d (m)
-Q
ra
E
N
-0.5
log(<K >) (m2 s"1)
log(s) (W k g '1)
-Q
ra
E
N
180.26
180.28
180.3
(yearday)
180.34
180.32
Figure 3. D e p th -tim e series o f T and com puted turbu len ce param eters d uring 2.4 hours around h igh-w ater, a. O bserved T-data. b.
S table stratification after reordering a. to stable profiles every tim e ste p and using S p= —0.23ST kg m ~ 3 °C_1 (see text), c. O verturning disp lacem en ts
follow ing com parison of a. with its reordered d ata. d. Time series of vertically averag ed ed d y diffusivity using (2). e. T urbulence dissipation rate,
estim ated using (1). W hite also indicates values below threshold.
doi:10.1371/jo u rn al.pone.0032535.g003
the large w a rm ing w ave nearly reaches the b o tto m (day 180.325—
180.333). A t 0 .3 -0 .4 m strong stratification is found (Nmax =
10_1'2±o' 1 s- 1 ; (TN)min = 7 5 ± 1 5 s) below a w a rm (Fig. 3a) weakly
stratified, tu rb u le n t core (Fig. 3b-e). T h e large, —h a lf h o u r p erio d
w ave contains m ultiple sm aller, weakly stratified waves.
the open sea possibly gen erated over the u n d u latin g sloping
bottom ; except th a t IW -beach-turbulence is sm aller in m agnitude.
D u rin g a n o th e r p e rio d w ith sim ilar stratification, ban d s o f
different surface sm oothness w ere visually observed a t the surface
com ing in from the northw est a t a n estim ated speed o f 0.04 m s 1.
E m ploying a tw o-layer internal w ave m odel results in a phase
speed o f 0.03 m s 1 a t given N , w hich is typical for in tern al waves
in shallow w aters (e.g., [20]). T h e m o d erate turbulence beachvalues are likely due to absence o f large scales found in the deepocean. T h e 1-2 m w ater d e p th lim its overturns to a n m is
O zm idov scale < L o > = 0.15 m , L o = ( s / N 3)13" — d. T his L o is
a b o u t 100 tim es sm aller th a n found in 550 m over large
topography, ju st like K z, roughly suggesting a linear d ependence
betw een K z a n d Lo- I f so, we m ay p aram ete riz e N = K Z-1
follow ing d — (K Z/ N ) 1/3 from (2), b u t we note variability in space
a n d tim e can be very large, by several orders o f m agnitude.
F ro m this b eac h ex p erim ent we lea rn th a t com m only rugged
shallow seas like the southern N o rth Sea can stratify d u rin g b rie f
periods a n d are n o t w ell-m ixed year-ro u n d , w hich is som ew hat in
contrast w ith predictions for seasonal stratification variations using
bulk p a ram ete rs [21]. T his sm all-scale stratification ham pers
vertical tu rb u le n t m ixing o n the one h a n d b u t also supports
m otions in its interior, w hich g enerate sufficient vertical exchange,
Discussion
T h e q uantified tu rb u le n t m ixing o f K z = 10 4-10 3 m " s 1 due
to convection a n d IW n e a r T exel-beach is one o rd e r o f m agnitude
larger th a n found in the o p en ocean, w hile its overall m ean,
ballpark p a ram ete riz atio n value, o f 2 x IO-5 m~ s-1 equals typical
o pen-ocean value [17,18], T h e associated overall m ean
< s > = 6 x l 0 -8 W kg- 1 . T h is IW -m ixing is tw o-three orders o f
m agnitude sm aller c o m p a red to S W W -breaking th a t is norm ally
found a t T exel-beach u n d e r average w ind conditions, b u t it is
th ree orders o f m agnitude larg er th a n m olecular diffusion. IW turb u len ce is not driven b y the atm osphere, as w ind-stress a n d
evaporative convection do n o t reach rapidly so deep w hen the
w ater colum n w arm s on a sum m er-day. T h e b eac h observations
resem ble, in IW -groups, IW -asym m etry a n d KFl-billows, m uch
larger (10—40 m high) IW -breaking over deep-ocean large
top o g rap h y [15,19]: this suggests b each -IW shoal com ing in from
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Internal Wave Turbulence Near a Texel Beach
e.g., to m ain tain grow th in the p hotic zone. T h e beach-site is
useful for investigating SW W -IW -turbulence interaction a n d
characteristics including fronts, convection a n d shear instabilities.
F u tu re experim ents will include salinity a n d c u rre n t m easure­
m ents, a n d T -sensors m o u n te d o n several poles to obtain
in form ation o n 3D p ro p a g atio n a n d evolution o f IW -turbulence.
U sing high-resolution T -sensors we have evidenced th a t the
Italian m others are right, o f course, in sensing n a tu ra l variability in
the sea interior. A lready in a cool sea such variations n e ed only be
0 .5 .1 °C to be sensed by hum ans. T his T -difference provides
stratification th a t is too w eak to b e a m echanical h a z a rd to
sw im m ers, w ho will lose only < 5 % o f th eir energy to g enerate IW
by their action [22]. T h e y are likely m ore h a m p e red b y the shock
o f 1°C+ T -difference w h en naturally gen erated IW pass; th a t is,
n e a r a T exel-beach in early sum m er, as in the A driatic cooler
blobs m ay b e felt m o re refreshing.
A cknow ledgm ents
W e thank R. D aalder for building the instrum entation pole an d A.
M argiotta, A. Souza and J. Kuhtz-Buschbeck for inform ation. W e thank
the anonym ous reviewers for their com m ents and advice.
A uthor C ontributions
Conceived and designed the experiments: H vH . Perform ed the exper­
iments: M vH EvH IJA G . Analyzed the data: H vH LG. C ontributed
reagents/m aterials/analysis tools: ML. W rote the paper: H vH LG IJA G .
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March 2012 | Volume 7 | Issue 3 | e32535