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Internal Wave Turbulence Near a Texel BeachHans van H aren1*, Louis Gostiaux2, M artin Laan1, Martijn van Haren3, Eva van Haren3, Loes J. A. G erringa11 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

AbstractA su m m e r b a th e r en ter ing a calm sea from th e beach may sen se a lternat ing w arm an d cold water. This can be felt w h en moving forward into th e sea (Vertically h o m o g e n e o u s ' and 'horizontally different'), b u t also w h en s tand ing still b e tw ee n one 's feet a n d bod y ('vertically different'). On a calm sum m er-day , an array of high-precision sensors has m easu red fast tem p e ra tu re -c h an g e s up to 1°C near a Texel-island (NL) beach. The m ea su re m e n ts sh o w th a t sen sed variations are In fact Internal waves, fronts and tu rbu lence , su p p o r te d in part by vertical s table stratif ication In densi ty ( tem pera ture) . Such m otions are c o m m o n in th e d e e p ocean, b u t generally no t in shallow seas w h e re tu rb u len t mixing is ex p ec te d s trong e n o u g h to h om ogen ize . The internal beach-w aves have am pli tudes ten- t im es larger th an th o se o f th e small surface wind waves. Quantifying their tu rb u len t mixing gives dlffuslvlty es t im a tes of 10- 4 - 1 0 -3 m 2 s - 1 , which are larger th an found In op e n -o ce an b u t smaller th an w ave breaking ab o v e d e e p sloping top o g rap h y .

Citation: 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; Accepted January 31, 2012; Published March 5, 2012

Copyright: © 2012 van Haren et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted 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.

Com peting Interests: The authors have declared that no competing interests exist.

* E-mail: hans.van.haren@nioz.nl

Introduction

T h e present oceanographic view is that in shallow w aters o f only a m etre deep, tem perature (T) m ust be hom ogeneous by turbulent tidal and w ind mixing. In contrast, w hen asked, Italian m others, lazily chatting in w ater up to their waist in sum m ertim e Adriatic Sea while overlooking their offspring, experience not a constant w ater tem peratu re bu t slowly alternating w arm an d cooler blobs o f varying height [M argiotta, pers. com m .., 2011], Now, this is an area w here surface w ater tem peratures reach T w = 29"C, n ear the range of neutra l h um an am bient skin-tem perature at w hich bo th w arm and cold fibers are active. H u m an therm oception starts at 0 .5 -T C T-difference, from physiology experim ents o f small body- surfaces a round 32"C [1-3], bu t body cooling reduces local therm al sensitivity [4]. How ever, regular beach visitors in countries like the N etherlands (TW< 20"C ) confirm : slow m inute- like T -variations can be sensed, w hen seas are calm.

H ere we investigate using high-resolution T-sensors w hether bathers in the N orth Sea experience physical phenom ena like ‘fronts’ and ‘internal waves’ and w hat tem peratu re differences their bodies sense under relatively cold conditions. Such physical phenom ena com m on in the ocean interior have never been quantified close to shore. T h e present study proofs suppositions about shorew ard extent o f internal waves from historic observa­tions in > 5 m w ater off Scripps and O ceanside piers in the Pacific [5,6].

As seas (and oceans) are heated from above an d w arm w ater is less dense (“lighter”) th an cold water, 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 that basically go unnoticed at the sea surface: internal waves (IW) w hich propagate m uch slower bu t with m uch larger

am plitudes th an surface w ind waves (SWW). Density stratification ham pers vertical tu rbu len t exchange of heat an d nutrients due to its stability. C ounteracting destabilization occurs internally, as IW m ay break, and even m ore energetically n ear lower an d upper boundaries due to (tidal) curren t friction at the bo ttom and atm ospheric cooling and w ind shear stress a t the surface. For the southern N orth Sea, winds, SW W -breakers and > 0 .4 m s 1 tidal currents are com m only thought to m ix solar heating from surface to bottom year-round [7], except for fresh-water outflows.

W e will show that IW can occur even at one o f the windiest spots o f the N etherlands, n ear a beach o f Texel-island. This is w here norm ally SW W -breakers reside, except after a prolonged period o f fine days for the entire region w ith strong insolation that is not m ixed away by atm ospheric and tidal boundary stresses. W e quantify the ra te o f tu rbu len t m ixing by these ‘beach-IW ’.

M aterials and M ethods

No specific perm its were requ ired for the described field studies. No specific permissions were required to perform N IO Z m easurem ents at Texel beach. T h e location is no t privately- ow ned or pro tected in any way. T h e field studies did not involve endangered or pro tected species.

A total o f 36 ‘N IO Z 4 ’ self-contained tem perature (T) sensors sam pling at 2 H z, w ith precision bette r th an 0 .0 0 TCI [8], were m ounted at 0.042 m vertical intervals on a w ooden pole (Fig. 1). T h e lowest sensor was 0.13 m from the bottom . Tw o sensors failed, including the lowest. T h e pole was fixed to the sandy, slightly undulating and weakly sloping bo ttom using two concrete slabs, w eighing ~ 4 0 kg each (in air). O n six selected days o f calm w eather and small SW W it was m oored a t 53" 02 .944 'N , 04" 42 .800 'E (near Texel beach-pole 13), H = 0 .6 m a t low-water

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dK z = 0 .128d2N . (2)

4—__________ J L1 A 1I. a . M

Figure 1. Instrument pole (upper sensor 1.60 m above the bottom ) near Texel beach with shoreward small surface wave breakers (thin w hite line close to the beach), a. Along-beach view, b. Beach-view with differential w ater tem pera tu re sensing. The pho tos are taken an hour before low-water. doi:10.1371/journal.pone.0032535.g001

(LW), during periods varying from half an hour to nearly a tidal period w ithin a span o f 14 days in Ju n e /Ju ly 2010. A t Texel beach we do not need specific perm its for w ater tem perature m easure­m ents. This tim e-span covered an atm ospheric high-pressure system over the region and calm, w arm w eather. D istance to shore (high-water, H W , mark) was approxim ately 100 m. Predicted tidal range is 1 .8± 0 .2 m, w hich includes spring-neap variation. M eteorological data are available from airpo rt D en H elder (15 km southward). SW W am plitudes and periods are estim ated from air-w ater surface passing the T-sensors.

T h e T -d ata 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 under local conditions. Lacking salinity (S) da ta it is assum ed that only tem perature contributes to Sp. As will be shown in Section 3, evaporation (salting the surface) contributes less to density th an heating. Differential horizontal advection will reinforce solar heating stratification, because in sum m er the fresher inland tidal-flat W adden Sea, bordering Texel on its eastern side, is w arm er than the saltier N orth Sea [9], H ence, the above density-tem perature relationship is a conservative one.

V ertical tu rbu len t eddy diffusivity K z and tu rbu len t kinetic energy dissipation rate s are estim ated by calculating ‘overturning’ scales using T -data. These scales are obtained after reordering every tim e-step potential density (tem perature) profile, w hich m ay contain inversions, into a stable m onotonie profile w ithout inversions [10,11], After com paring raw and reordered profiles, displacem ents (d) are calculated necessary for generating the stable profile. A certain threshold applies to disregard apparen t displacem ents associated w ith instrum ental noise. This is very low for N IO Z -thern iisto r data, < 5 x l 0 -4 "C [8], T hen,

g = 0 .64d2N 3, (1)

w here N denotes the buoyancy frequency com puted from the reordered profile an d the constant follows from empirically relating the overturning scale w ith the O zm idov scale L o = 0.8d [12]. LTsing K z = T sN -2 and a m ixing efficiency for conversion of kinetic into potential energy o f T = 0.2 [13], we find,

Results

D uring the fortnight o f observations, w ater w arm ed steadily on average. T h e short-scale p henom ena to be described here were observed in all six records, although w ith some variations in intensity. W e analyze the longest observation period o f 11 hours on 30 Ju n e 2010 (yearday 180). T h e pole was m oored around 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 perature T a< T „ an d in sea no T-differences w ere observed (Fig. 2). C loud- cover rem ained high (60-100%) the entire day, with some sunshine betw een days 180.3 an d 180.4 w hen hum idity reached a m inim um o f 80%. A daily evaporation sum of 0.7 nini is calculated for these conditions [14], im plying a salting o f 0.02 PSLT m. T o balance this density contribution one requires ~ 0 .D C of w arm ing; the observed tem perature differences were m uch larger. Potentially stratification counteracting, fresh g round w ater leakage is found little im portant, as it w ould generate free convection in the overlying saltier sea w ater, hence com plete hom ogenizing. T a,max= 22uC around day 180.55, w hen the easterly w ind-speed equaled 4—5 m s *. Such winds could increase stratification in concert w ith lateral density gradients, bu t variations as presented below were also observed during periods o f no wind. Easterly winds created only small surface waves n ear the pole, as the beach is exposed to the W est. SW W -height including swell was about 0.1 m (Fig. 2a, yellow bar) with 3-10 s periods.

T-observations in the sea (Fig. 2a) varied betw een 17.05 and 18.97"C (in saturated to the right). In the beginning o f deploym ent w hen T a< T w, stratification was very weak, although the upper layer was still 0.03"C w arm er th an near-bottom , and occasionally even, apparently unstable (cool above warm). As soon as T a> T w, well-stratified w ater passed T-sensors that were now all below surface (at H W sea level is about 0.90 m above the highest sensor). A round H W m ore than 1UC w arm er w ater passed in different ways: slowly varying with periods o f a few hours (Fig. 2a after day 180.265), w ith periods o f ha lf an hour (180.30-180.38) and m ore rapidly with changes every 60 -9 0 s (Fig. 2b,c): trains o f IW with vertical am plitudes varying betw een 0.2 and > 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 perature differences were sensed by team m em bers, regularly swim m ing or standing in the sea n ear the pole w ithout disturbing the m easurem ents (Fig. lb).

H eating from the atm osphere does not directly force IW , as stable w arm w ater initially spreads like a pancake over colder water. IW -am plitudes are m uch larger than SW W ’s and their periods 0 (1 0 0 -1 0 0 0 s) are m uch longer than 10 s.

Details show that irregular internal m otions also occur that can have periods o f 10-30 s (Fig. 2b,c). T hese cannot be in terpreted as freely p ropagating IW , as local stratification has a smallest buoyancy period o f T N~ 6 0 s w hen calculated in extrem ely thin layers < 0 .1 m, even though using the conservative density- tem perature relationship. Instead, these short-period m otions represent turbulent overturns, e.g., day 180.3346 (Fig. 2b) and days 180.2876, 180.2912 (Fig. 2c), following different (IW-) currents above an d below shearing an interface and rolling it up. T hese overturns have periodicities betw een IW an d SW W [15]. Shear m agnitude ( |S|) is not m easured here, bu t extrapolating from historic central N orth Sea observations [16], we can expect |S |~ N ~ O ( 1 0 -1 s-1 ).

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180.2 V Tw 180.3 HW 180.4 180.6180.5

I1000 s

12 (hh:mm UTC) 14:249:36

180.335180.334 180.336

7 " ^ w

_q

E

17.2

180 .288 180.289 180 .29(yearday)

180.291 180 .292

Figure 2. Almost one tidal period overview of detailed tem perature (T) variations near Texel beach in early summer. The vertical scale is 1.75 m with reference to the bottom . For display purposes, the colour-scale does not com pletely cover the observed w ater tem pera tu re range of [17.05,18.97]°C. a. The small red bars indicate zoom s in b., c. and the large one indicates th e period o f Figure 3. The vertical red-in-white line indicates w hen Ta = Tw using upper therm istor in w ater and atm ospheric da ta from Den Flelder-airport. The black dashed curves indicate th e predicted tidal sea-level height variation (sensors in air above it) and th e yellow bar on th e left spread of surface wind wave height, estim ated from th e w ater surface passing T-sensors. Time (UTC) is 0.33 hours before local SolarTime. b. Zoom of a front and trailing 80 s period IW and shorter period IW -turbulence m otions, c. Zoom of high-frequency (60 s period) internal w aves and shorter scale overturning. doi:10.1371/journal.pone.0032535.g002

A transition betw een w arm and cold w ater passes, w hich is m ore th an 1.2 m in height (Fig. 2b). It m imics a frontal passage, like in the atm osphere. N ear the bottom it seems to be unstable (Fig. 2b, day 180.3345: w ater n ear the bottom w arm er than halfway up) and m ay thus break thereby generating turbulence. T h e “waves” riding the near-bottom stratification are not propagating IW , bu t have SWW- am plitudes and periods: pum ping up- and down the w ater colum n. T h e larger am plitude and -period front-trailing waves include asym m etric turbulence-like motions.

A train o f finescale IW w ith tu rbu len t m ixing cores and overturning (Fig. 2c) shows every m inute T -variation o f 0.5"C across ~ 0 .5 m in the vertical.

W e quantified this tu rbu len t m ixing (Fig. 3). U ntil day 180.265 (Fig. 3a; red-in-w hite line indicates independent estim ate T w = T a) the near-hom ogeneous layer (Fig. 3a,b) is weakly stable with occasional overturns (Fig. 3c). T his m ixing is likely driven following nighttim e air-sea interaction. It provides vertical average

< K Z> = 1—3 x l 0 -5 m~ s“ 1 (Fig. 3d). T h e associated heat filix (not shown) and turbulence dissipation ra te (Fig. 3e) are no t very large (s< 1 0 8 W kg *) because stratification is so weak.

Transition (day> 180.265; T a> T w) is ab rup t from weak to strong stratification. After an overturning front, turbulence param eters drop one-tw o orders o f m agnitude, even though T - variation is initially a few tenths o f degrees. How ever, periods w hen turbulence approaches 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 and th rough the entire range small spots o f < K Z> ~ 1 0 5 m~ s *; s —10-8 W kg-1 are observed. These spots are associated with short-period weak IW -overturning. IW -am plitudes, stratification and 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 upper ha lf o f the observation z-range.

After day 180.31, w hen larger-scale IW moves up an d cooler bo ttom w ater move in, turbulence becom es w eaker (in Fig. 3) until

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Internal Wave Turbulence Near a Texel Beach

-Q<UEN

.ÛroEN

-QraEN

-QraEN

180.26 180.28 180.3 180.32(yearday)

180.34

18.2

18 T(°C)17.817.6

117.4117.2 1 - 1

-1.5

2

-2.5

log(N) (s'1)

.1

0.5d (m)

-0.5

log(<K >) (m2 s"1)

log(s) (W k g '1)

Figure 3. Depth-tim e series of T and computed turbulence parameters during 2.4 hours around high-water, a. O bserved T-data. b. Stable stratification after reordering a. to stable profiles every tim e step and using Sp= —0.23ST kg m ~ 3 °C_1 (see text), c. Overturning displacem ents following com parison of a. with its reordered data. d. Time series of vertically averaged eddy diffusivity using (2). e. Turbulence dissipation rate, estim ated using (1). White also indicates values below threshold. doi:10.1371/journal.pone.0032535.g003

the large w arm ing wave nearly reaches the bo ttom (day 180.325— 180.333). At 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 arm (Fig. 3a) weakly stratified, tu rbu len t core (Fig. 3b-e). T he large, —h alf hour period wave contains m ultiple smaller, weakly stratified waves.

Discussion

T h e quantified tu rbu len t m ixing of K z = 10 4-10 3 m" s 1 due to convection and IW n ear T exel-beach is one o rder o f m agnitude larger th an found in the open ocean, while its overall m ean, ballpark param eterization value, o f 2 x IO-5 m~ s-1 equals typical open-ocean value [17,18], T he associated overall m ean < s > = 6 x l 0 -8 W kg- 1 . T his IW -m ixing is tw o-three orders o f m agnitude sm aller com pared to SW W -breaking th a t is norm ally found a t T exel-beach under average w ind conditions, bu t it is three orders o f m agnitude larger th an m olecular diffusion. IW - turbulence is not driven by the atm osphere, as wind-stress and evaporative convection do no t reach rapidly so deep w hen the w ater colum n warm s on a sum m er-day. T h e beach observations resem ble, in IW -groups, IW -asym m etry and KFl-billows, m uch larger (10—40 m high) IW -breaking over deep-ocean large topography [15,19]: this suggests beach-IW shoal com ing in from

the open sea possibly generated over the undulating sloping bottom ; except th a t IW -beach-turbulence is smaller in m agnitude. D uring ano ther period w ith similar stratification, bands of different surface sm oothness were visually observed at the surface com ing in from the northw est a t an estim ated speed o f 0.04 m s 1. Em ploying a two-layer internal wave m odel results in a phase speed o f 0.03 m s 1 a t given N, w hich is typical for in ternal waves in shallow waters (e.g., [20]). T h e m oderate turbulence beach- values are likely due to absence o f large scales found in the deep- ocean. T h e 1-2 m w ater dep th limits overturns to an m is O zm idov scale < L o > = 0.15 m, L o = ( s /N 3)13" — d. This L o is about 100 times smaller th an found in 550 m over large topography, ju st like K z, roughly suggesting a linear dependence betw een K z and Lo- I f so, we m ay param eterize N = K Z-1 following d — (KZ/N ) 1/3 from (2), bu t we note variability in space and tim e can be very large, by several orders o f m agnitude.

From this beach experim ent we learn that com m only rugged shallow seas like the southern N orth Sea can stratify during brief periods an d are no t well-m ixed year-round, w hich is som ewhat in contrast w ith predictions for seasonal stratification variations using bulk param eters [21]. This small-scale stratification ham pers vertical tu rbu len t m ixing on the one h an d bu t also supports m otions in its interior, w hich generate sufficient vertical exchange,

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Internal Wave Turbulence Near a Texel Beach

e.g., to m ain tain grow th in the photic zone. T h e beach-site is useful for investigating SW W -IW -turbulence interaction and characteristics including fronts, convection and shear instabilities. Future experim ents will include salinity and cu rren t m easure­m ents, an d T-sensors m ounted on several poles to obtain inform ation on 3D propagation and evolution of 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 na tura l variability in the sea interior. A lready in a cool sea such variations need only be0 .5 .1 °C to be sensed by hum ans. This T-difference provides stratification th a t is too weak to be a m echanical hazard to swimmers, who will lose only < 5 % o f their energy to generate IW by their action [22]. T h ey are likely m ore ham pered by the shock o f 1°C+ T-difference w hen naturally generated IW pass; th a t is,

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near a T exel-beach in early sum m er, as in the A driatic cooler blobs m ay be felt m ore refreshing.

A cknow ledgm entsWe thank R. D aalder for building the instrumentation pole and A. Margiotta, A. Souza and J. Kuhtz-Buschbeck for information. We thank the anonymous reviewers for their comments and advice.

Author ContributionsConceived and designed the experiments: H vH. Performed the exper­iments: M vH EvH IJA G . Analyzed the data: H vH LG. Contributed reagents/m aterials/analysis tools: ML. W rote the paper: H vH LG IJA G .

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