Langmuir Parameterizations Baylor Fox-Kemper and Adrean Webb CIRES/University of Colorado at Boulder In preparation for continued research with Keith Julien, CU-Boulder; Greg Chini, UNH; E. Knobloch, UCB 13th CCSM Meeting--OMWG Session Thurs. 6/19/08 11:25-11:40 Langmuir, What? January 31, 2008 3:55 Geophysical and Astrophysical Fluid Dynamics cjkLC 2 Fox-Kemper et al.: Windrows 12 March 2008 2 Reduced Model of Langmuir Turbulence Figure 1. Images of Langmuir circulation windrows: (a) a photograph of Rodeo Lagoon in CA (Szeri 1996), (b) an infrared image of Figure 1theImsuragesface ooff TLangmampa Bauiry (ccirculourtesationy of G.windroMarmows:rino, (a)NRLa, Dphotograph.C.), and (c) oftheReovodeolutioLagon of sonurfaince CAtracer(froms in a LSzeri,ES of L1996),angmuir : turbulence (McWilliams et al. 1997). (b) an infrared image of the surface of Tampa Bay (courtesy of G. Marmorino, NRL, D.C.), and (c) the evolution of surface tracers in a LES of Langmuir turbulence (McWilliams et al., 1997). Reproduced from Chini et al. (2008). 1 Introduction by theLaco-inngmvuesirtigatorscirculati(Chini,on (LC)2008;is a wChiniind aetnd al.,surface-willwavbeeddorivcumenen conted,vectandive fltheow groundwthat comorkmofornlyimple-occurs in 2008).thHoe uwpepveer,r labyeforeers ofsplaendingkes, rivtimeers anond oacecom-ans (Leibmenovictationh 1983of, Ta hfullorpparameterizatione 2004). When thwille wbinedlaid.s exceed a plex mofewdelmiteteisrsimpperortansecontdto, LdetermineC exhibitsthea ralikngelye of length and times scales, from centimetres to hundreds of magnitudemeterofs aclimatend secoimndpacs tot.hTheoursresearc. The ehmplanergenis:ce of a4.broaBudgetd spectrum of scales prompted McWilliams et al. (1997) to dub this phenomenon “Langmuir turbulence,” both to emphasize that LC is properly viewed as Formpartulateof thane upalgebraic,per oceanequilibratedturbulence aapprond toxi-distingProf.uish itFforx-Kempom waller-borequestsunded sh1.5earmonflowthsturofbusummelence. Evr en • mationunder ofuntheconLangmtrolled,uirstrcirculationongly superduecrititocaChinil environmsalaryental cforondhimselfitions, handowe1.5ver,monLCthsis doofmsuppinateortd bfory enoneergetic (2008).counterThis-rotaparameterizationting streamwise vowillrticaincludel structtheures. Thpre-compsese structuappliedres are emathlongatgraduateed in the wstudenind ditreatctio50%n when mixedthe wilanyder-drdeepivenesninghear scalingand surfofaceLi-wandave SGar-tokes dri(approft are ximatelythemselve$18ks aligtotalned wincludingith the wifringend or btoenefitsthe right rettof th(1997)e windanddirecbteioconsistenn when Ctorwithiolis eLangmffects auirre signibutficannott. Inindirecview tofcosts).this evident anisotropy, the aim of the turbulencepresent stusimdyulationsis to de(re.g.ive ,aMcWilliamscoarse-graineted,al.,quasi-three-dimensional description of Langmuir turbulence. REFERENCES 1997).Figure 1 shows several illustrations of the hallmark surface signature of LC: a series of roughly parallel, Chini, G. P.: 2008, Strongly nonlinear Langmuir circulation Implemenwind-aligtnthised stapproreaks.ximateThese “parameterizationwindrows” are evident visuaandllyRa(fiyleiggurh–eB1´ena(a)rd), coinnvinectiofran.resubd amittend adctoouJournalstic imofagery • in(tofiguthere 1NCAR(b)), anCommd in fuunitll thyreClimatee-dimensSystemional (3D) directFluidnumMeerichanicscal an.d large-eddy simulations (DNS and MoLESdel., respectively – figure 1(c)). To date, the vast mCahini,joritG.y Po.,f K.nuJulien,mericaalndsiE.muKnolatbloioncsh:o2f00L8C, Anhaavsyme eptompti-loyed cally reduced model of Langmuir turbulence. submitted to Pterformhe Craiak–sensitivitLeibovicyh (testCL)ineqaualotiw-resolution,ons, a surface-wave filtGeereophysicd versalioandn ofAstrthophysice NavialerFluid–StokDynamices (NSs). equations; • ocean-onlysee Craik,anconfigurationd Leibovich (with1976)simplified, Craik (19w77a)vaend LeiCbraoik,vicA.h (D.19D.:77)1. 9T77h,eGeCneraL eqtiounatoifoLansngamreuirfocircularmalltioy insdebnytical to the instantaneous NS equations apart from the occuanrrinstaencebilitofyamvecohartnismex-f.orJournalce termof gFluidivenMebychanicthe sc,ross forcing. 81, 209–223. product of the Stokes (or Lagrangian mass) drift velocity, associated with the high-frequency waves, and Continue sensitivity testing including higher- Fox-Kemper, B., G. Danabasoglu, R. Ferrari, and R. W. Hall- • resolution,the filteredrealisticvorticitwyavecforcing,tor in thande wacoupledter column. ThebCergL: 2v0o0r8t,ePxarafomreterizingce captsubmesoures thscae lerephctysicsifiedinegffloebactls of the filtered waves on the time-averaged dynamics. Numclimaeroutes imonvdels.estigCLIVatorARs, inExcsphangeired sb,y13t,h3e–5a.ppearance of models as necessary based on early results. Fox-Kemper, B. and R. Ferrari: 2008, Parameterization of the locally parallel windrows, have carried out theoretmicixedal stlauyderieeddies.s andII:nuPromegnoricsisal asndimimpaulatct.ionJournals of thofe 2D It should(genbeeraplossiblely downtowicompletend invariathisnt) proCLjectequawithintions; see e.g. LPhysiceibovialchOc(e1ano985gr)aphy, Le,ibinovpress.ich et al. (1989), Cox et al. a short(1time992a)frame,, Cox ewitht al. preliminary(1992b), Coxresultsand Lbeyibothevich (19La94ng),mCuir,hinI.:i a1n93d8,LSurfaeibocevimchotio(2n00of3w),aterChinducedini andbyLweiind.bovich (2005), Li and Garrett (1993), Gnanadesikan and WelScleier nc(1e9, 9875,) 1a19n–d123L.i and Garrett (1997). With the end of summer, 2008. Large, W., J. McWilliams, and S. Doney: 1994, Oceanic ver- exception of the secondary stability analysis of TandonticaanldmixingLeib:ovAicreviewh (199a5nd), ahomwoedelverw,ithinvaevsterticaigatliok-ns of the stability of 2D roll solutions of the CL equations topro3fileD dboisundaturbryanlacyeers paharavme eterizabeentioren.strRiecvt.edGetophys.o we,akly 3. Summarysupercritical forcing conditions, where weakly nonlinear36o3r–4s0m3.all wavenumber (i.e. large cell aspect-ratio) Leibovich, S.: 1977, Convective instability of stably stratified An estimationapproximaoftiothens ceaffnectsbe uoftiliLangmzed (Cuirox acircula-nd Leibovich 1997w,aterBhinasthekaroacean n.anJournald LeibofovFluidich 2Me00c2hanic). s, 82, 561– tion on global climate is proposed. If sensitivity is 581. Li, M. and C. Garrett: 1997, Mixed layer deepening due to found in regions of climatic importance, it will sup- langmuir circulation. Journal of Physical Oceanography, port conItinn tuationhis inveofstiagahighlytion, wineterdisdevelciplinaryop a stroncol-gly nonlinear27q,u1a2s1i–-133D2. approach that relaxes the assumptions laborationof str(fourict dospwnewcialitieind insvaarerianrepresence and wtedeakbysuthepercriticaMcWilliality yemt s,exJ.ploCi.,tsPt.hPe. sSullivlow adn,owanndwiCn.-H.d vaMoriaengbi:lit1y99o7f, the Langmuir turbulence in the ocean. Journal of Fluid Me- investigators),appropriaandtely bringcoarsedev-graelopmenined flotsw.atSptheecificut-cally, we obtacihanicsn a re, d334uc,e1d–3d0.escription of Langmuir turbulence ting edge of applied mathematics into practical use Smith, J.: 1998, Evolution of Langmuir circulation during a in the world of global climate modeling. A novel cli- storm. Journal of Geophysical Research-Oceans, 103, 12649–12668. mate sensitivity with potentially substantial impact Deep.Sea Research, Vol. 35, No. 5, pp. 711-747, 1988. 0198-0149188$ 3.00 + 0.00 Printed in Great Britain. ~) 1988 PergamonP ress plc. Langm*REPORTSuir, do we care? Role of Langmuir Circulation in the Deepening Abwater,is theh isbuoyancythe depthjumpof theatmixedthe baselayer,of andthe Langmuir circulatiofonthe wiOceanthin thSurfacee oceanMixedic miLayerxed layer layer. Using model results for Wdfn/U*, this means that Langmuir circulation will deep- Maybe: Ming Li,* Konstantin Zahariev, Chris Garrett en the mixed layer until ROBEHelicalRT Amotions,. WEknownLLEasR*Langmuir a n d circulation,JAMES areF.a keyPRphysicalICE* process in the upper Ab = cu*/h (2) ocean but have not yet been incorporated into ocean models. Here, surface mixed layer where c = 0.72SJ(v1); values for v were deepening by Langmuir circulation was added to that due to convection or velocity adjusted to match vertical velocities be- shear; Langmuir circulation is more important than shear if the velocity difference tween the model results and observations (Received 15 June 1987across; in revisedthe mixed-layer form base23 Novemberis less than about 1987;1 percent acceptedof the wind 27 Novemberspeed. In an upper 1987) (9-12). We estimate that c 50 for fully ocean data set, evidence was found for the deepening of the mixed layer by both developed seas, although it may be signifi- Deep.Sea Research, Vol. 35, No. 5, pp. 711-747, 1988. 0198-0149188$ 3.00 + 0.00 Printed in Greatmechanisms. Britain. Thus, Langmuir circulation influences upper ocean diurnal and~) 198seasonal8 PergamonP rescantlys plc. smaller in developing seas (1 1). Equa- changes in stratification. tion 2 is similar to that of an entrainment Abstract--The three-dimensional flow in the mixed layer associated with Langmuir circulatmodelion based on u* (13), but our formula is was studied with a new instrument capable of directly measuring the three componentsbased of on process modeling of Langmuir cir- culation (which was not present in the lab- velocity. Regions of converItgehasnt beensurfoverace 50floyearsw wsinceere Langmuirlocated wperature.ith surHere,face wedrattemptifters.to Iestablishn thesethe regioratoryons experiments), and the coefficient c the downward vertical and describeddownwwind-inducedind horizovorticesntal cinomtheposur-nentsrole ofof thLangmuire flow