Office of Naval Research Navy Department Contract N7 onr 487 T.O. 3 Project NR 083-061 ee oe Geophysics Branch Technical Report No. 6 eo John C. Freeman, Jr. October, 1953 ~ Research Conducted through the te ee - Cexas A.&M. Research Foundation oe COLLEGE STATION, TEXAS Paes Nn iii ANION i O 0304 The Agricultural and Mechanical College of Texas Department of Oceanography College Station, Texas Texas A & M Research Foundation Froject 29 WIND MIXING CURRENTS (Technical Report No. 6) Project 29 is a study of the atmospheric influence on the thermal structure of the oceans, sponsored by the Office of Naval Research (Project NR 083- 061, Contract N7onr-487, Task Order 3), October, 1953 Prepared by JOHN C. FREEMAN, JR. Maybe): Ne ATR Hwnenelh itiett eit 8d ABSTRACT A wind system may create an ocean current by differential mixing in a two layer ocean; such a current may be imposed on other currents due to the wind through effects of stress, piling up of water and mass transport by waves. In one situation studied, such differential mixing produced an average transport of water aktout ten to twenty percent of the transport due to wind stress. WIND ACTION ON THE CCEAN Sverdrup*has summarized the processes through which wind causes currents in the ocean: a) currents directly driven by wind stress b) currents indirectly maintained by piling up of stratified water ce) mass transport of water by wind waves. In addition to these effects on the ocean, wind also causes mixing between the cold thermocline waters and the warm surface layer of the ocean, The following discussion shows that through such mixing action the wind may cause an additional current (in an ocean with a stable density stratification). It will be assumed that a strong wind mixes more cold water upward into the warm mixed layer than does a weak wind. Observations tend to verify this; for example, in Figure 1 the bathy- thermograph trace of a ship at 45°N, 45°W for 8 October is contrasted * The Oceans, 1942, pp. 489-503. Y dante: iy Fi cee Fite’ (fata Ho peo » “s, vr nt aa 9 Hou 044 nahika vaprati aa soni 4 on Th Pans tia faust oan at | Hae ee eg la tye Heqarwn! pens erate hae yenaags baky od! ath Secon eat. as oD ae Nl i mies Waar ant (0 <6 gt) on , ; a iit agi dd Hs ortoesrany” geld aetna sae, Avi) ip) ie ae ; PM My hue 16008) ‘bese nb, ees % ar) oh ‘t 7 i ae geeité Lats ved oN: eon Lai site. % 4 EH ne cn sik RO) ie EMT ro Main 26 sent ee, Wi toanom rh u Oa ee sibel ae “| nt (yaa remer wet nbd! thy heh rained Ee « } ‘i ihr abi ecanns nate ‘hkl tious atl non edger | bean i bre haa (he. hie Ae ne omen Bath can Pea She f OORT TR hlen, Pie) eats ios “th. reine Joa SGos2 LOpAPORD ED) 2 mth wet i i OY PATS atts hawer fe yet) Aeeeeratea Saint ehh aT Haus yore ‘Holi isis ay ; mA P vo) Py quelt Yi Ly Al ‘ (eu ir ait ; f “ Oe a Aine pane attony naeam a DMA i a Pea RAN ty Wanninee ad fy in i ; 1 ih te r Lee a mY “ti He oy oR BD LAE veriap nia ir foe i butt aint | 7 i Posen i ; Nh eae! F ie i OM WN -vshtnt val Cara ree ae ea tu) vine od ing ae pista ny navihet att, ) sof Wes eek oe baa a i ial di AAACN RE an mR a ut POSER a Kia bee Ue ay ANT ae i age CNT an ; i Ve ay rs AM bert , ati } t ¥ ‘ | y om R } f i | Apes mii) Wie y { net nh i ei i} a 1) es Ri , tio) ne . =i Des with traces for 28 September and 18 September 1949. For the period 28 September to 8 October (period A) a wind averaging Beaufort 53 persisted; for the period 18 September to 28 September (period B) the wind averaged Beaufort 4. During period A the mixed layer temperature cooled almost 5° F and deepened about 110 feet, sug- gesting the upward mixing of a large amount of cold water into the surface layer from below the thermocline. For period B, however, the thermocline depth remained almost constant and the surface layer temperature increased, suggesting little or no mixing across the thermocline. Consider that a strong wind (and associated mixing across the thermocline) persists in one section of the ocean, while nearby a weaker wind occurs (causing little or no mixing), The colder water in the surface layer under the stronger wind will alter the density distribution in the surface layer. In response to this new density distribution, a current wili occur within the upper ocean layers. EVALUATING THE WIND MIXING CURRENT Assume that the ocean is a two-layer system with constant densities in the upper and lower layers. Strong winds over a portion of the ocean will then cause mixing across the thermocline (boundary) and a region of relatively cold water to be formed in the surface layer of the ocean, Neglecting the other wind effects, such a hori- zontal variation in the density distribution of the ocean surface layer will lead to a current. WA sa shh ve) a json) risen 2 oF ae (ipabine se ows se cans 2 84, etna yet ee (mae alin ke sk Hades me ele | ae bestia snpiova 4 a H a PbO np ee bh. 98 tachi avo: onli “aan uae a2 aah io ‘*6 fant ente oye 8 R aakiit See a owas feb 967 ‘ak Locantatt eit? ops art 10% alk BO a tedbia atl ew pyre! not rae isi iat enc | . eo ord hata: hee tamed decals boa hehe deat ond tes iW, ’ ie ay : ’ t re } } nit echo patton pudaanosne ‘Ben) bake goortta A) eee sateaht) vga ae hime 40 pad “to mibessa So os ad ab to (iano "ae n) oaeistas int Ggaivita | i git eatin LiKe betdy 09% port her gouge ay aget Abate a » : . (ah RAT @! suncgees .£ etree rhe’ nt dabeusiateel 7 i ry » ATWebs BOG THN SET AP oN aero ELEM saat Et no bhatt tsi wap efepet meebetiest } El bik an “ah ¢ * ay fi) 7 | Waney 4Y 0S BALMS! E) ne i TAN cA Vnndtdco driv wel ac LA Bet we 4 me, Calo HF Sond meee) tent eos thik: Rate ni aw yaptdaoy @iaute Shite qo, : . 7 1 ae (yt benenet) nist fy carreuls ans Raripe Ba hee bein Poe tt BKPID. 9 7 4 i) peg ae feel ret Paar? PT ee 16050 Glas tovh eg et i soins | 7 se by Bid We Ahad eo AOMA gs walt! be Rithw ORT add: Rabon! tant Pees Aas 1 eri vik nar’ / : qtits aiff ie a te Lisbon auetion naan aed os Pact ta faites : % f Htlie| ed After initial transient effects have disappeared, such a current will be in geostrophic balance so that fs IL) hs) uc a aire Se ay WA AILS Gis e} VE aI aE Vs IC) Aig (2) where u and v are the ocean velocity components in the x- and y- directions respectively, p' represents the ocean density at a given point (x,y) in the surface layer and p represents pressure. The hydrostatic equation is pi (=! pom BPLZ) > (3) where Po is atmospheric pressure at the ocean surface (assumed con- stant here), g is gravity and z is the depth (measured positive downward). We use this equation to obtains Qo! lL) eS ane a (4) ao! This whole process has not affected any pressure below the surface layer. Hence there is no current below the density discontinuity. Thus Margules formulae for the slope of density discontinuities on a rotating earth with (4) and (5) give the relationship: aE ie ea ee SE Dy ao oie! (6) ose Gay a) San and ve (yy = fH CH = & Sp! (7) ite) xe ig lichra ta where be =e o-p! These expressions assert that the current in p the mixed water at the interface is balanced geostrophically by the Len ae i) ie me Q niet yee Hi — { 5 -i- slope of the interface. We can show that this slope is a natural result of the mixing process. For the mixing process assumed here P' changes such that 4p! FF re (p-p') ° (8) Equation (8) tells us that since space changes exist because of mixing (9) This is essentially the same as equation (7). Thus the op bd - oO t SS wy Fae slope of the interface resulting from mixing balances the geostrophic current created by mixing. Some of the features of such a wind mixing current are shown in Figure 2. The assumptions are made that a steady wind uniform over the region is blowing over the right-hand portion, while a calm exists over the left portion of the figure. These conditions have prevailed for some time so that transient effects are no longer present. The density is constant in the vertical above and below the thermocline transition zone, although it varies in the x-direction. The induced current thus would produce the isobaric pattern shown. A geostrophic current would thus be directed into the figure, and would vary from zero at the top surface to a maximum at the deepest part of the transition zone. Figure 2 differs from Figure 1C6 in The Cceans (p. 446) in that Figure 2 shows a horizontal variation in density above the transition zone, while there is no such density transition in Figure 3 adapted from The Oceans. uate Vala” 6 k¥" rakes ibe rs a eal il h Gaia racket ig nee: PENA Me ure soiree peer Fes nif RE “i Heigl, pul bth weds ace toa aditint " i? i eae . feat fete aueesit! ee oC ene be waded ek “tb cane i ‘winapanal ewe eee Me 5) en iit fink ‘wild sl ee | esata iMate east eisatia swith Usaet bik eecsa: LA ohh BOP WERE RY Si, ij K ‘ MAES Te? StOmNeL ve npr urs ae bgt hi not shane a FR Gs uc ho Mock Aes anh ie bo Be sets Be nus Stys ot ees tg val aad : pane one dug, te Vs Meh Heke rt mR: Bek SHOW ; een ney j Per A Oly leh Me Ur hs ‘tt yin righ Raat! i me’ agi? meet : “i Oe aD ts [diene eth ee heii ii iy ai fiae Sea tae! ah? “os oe ‘ooh ih vith) PL Meare Hare dee ang AVAL ‘ayegil iy AOU al Nai [OWA Re ROU rae OE B15 ORDER OF MAGNITUDE OF THE WIND MIXING CURRENT Since the wind mixing current varies linearly with depth in the model above the total transport of water is = 1 2, (82H oo" 10 7 : a Gre = Go) sei et 82H apt EL 52 a cae (11) Considering data from which Figures 1 and 4 were taken* over the indicated intervals of time between Stations "C" and "D", assuming one-half the variation at "D" was due to mixing, the average transport due to wind mixing during the 10-day period 28 September to 8 Octoter was 0.4 ft/sec. The transport due to wind stress during this period could have been about 27 £t?/ sec, Hence it would appear that the wind mixing current is small compared to possibile wind stress currents, However, taking into account the direction of the wind, the resultant stress transport for this period was 2-5 £t*/sec. Thus the wind mixing current was ten to twenty percent of the net transport by the wind stress for this 10-day period. ACKNOWLEDGMENTS This work was stimulated by contact with Mr. H. Stommel and Mr. W. Malkus at the Conference on the Thermocline held at Big * Technical Report No. 3, "Summary of North Atlantic Weather Station Data", Project 29 Texas A & M Research Foundation, ONR Contract N7 onr 48703, NR 083-061, September 1952 i nna ue sain ts foto? ind ‘wt vi Cob ig (ht) ( xs) myedal sqhel N Sisk & wait: bay note ata “gabshbtasd ane nd Nt wen bagde erated. ants 36 "bkayaot via - * < _ OO IES \agptoeye itd SOL SLM ah xy | taetey Male th Mordatys aig “atest Rene Je ’ - | ‘setenculcpel! Ss elt ress ee ek AL) DS 0 aT eis tu fa Tetterat Or; one) Ryy Bu eo ee atssaht eS Kw oa wabis BREW Ss se ao 2 bv ) fy bi ome Biioy i Sang”. yet OPENS, remade) ee J. mesg 1 eae bie ; rr ‘ iy ‘f Ceerta bate gidteaot O0: Lewedon Line, ef Jor 0. et bait silt 4 ae a } . tah Sik. To. doktoest) ete:,.dptyoas odtis | SAL ARTS eorrenge ae ORS Sayre 5 a > : anc ro a 4 . . it i .¥ 14 tes ay 0 fT40 8 A G7 Sot eeqany "a ny oT aed ecu i : 3 5 Ppa yal o vaeertnat intel ‘oak , : ee Ma eee | Brtkw ¢ote ——— ¢ ~ : 4 ra Tie act ‘ W he | (ani nee Lu’ eel ta? ‘#YOK ‘i ’ , ; ' 7 asa os ot cht Logan wilt ; tee” sick See te , i Bey vo i Wa a . noeinae toacisgad nities dsc ts “Sita” as, ager hee oe ia) a ediind) TG napseceieys Hoty nh ewe hs : 2 . TOA es SPUN \opeaLathat yee | qlee GK) Si, tery aay aged Meadows Lodge, Virginia, 25-27 May 1953, and by work on Office of Naval Research Contract N7 onr 48703, Project NR 083-061. Messers, C. Sparger and G. Jung, members of the project, made significant contributions to the style and technical detail, rage" a uJ sy u E> , sii ar Migs de ate ru ms see Pst Te ere ee ae BS oF negeistaed, OF betaey old) gntaus getareew art fx vead srey ahirt: and Miri badness wetuetas?: ait iniots0 8S bon vedinde Bo ested A odd aboty) edt bas /Sniome aya l 2 vt | beloos mailed ONL BS Antigy Go treet okt \ LEGEND FIGURE 1 The warming during the period 18 September to 28 September occurred when the winds were Beaufort Force 4. Between 28 September and 8 Octoter the column cooled ty a large amount and the winds were Beaufort force 5 1/2. 60° 65° 7O° DEGREES FAHRENHEIT 100 150} 200 ie? ——— D 18 SEPTEMBER 1949 —-—- D 28 SEPTEMBER 1949 D 8 OCTOBER 1949 250 FIGURE | cicee i = - Soe weet = . sae 7 ~~ ~~ eT Oye a EER | > > a ~ —_ Talli eee hes Se ea ey = } 4 hei ti " = : \ i | j v4 x ; & RAT MP in Lee i fi J rf i f" f | ‘ SV ipod a y ies | acalaais wietialadls Veins ee i ; ‘ rur i c r } tame ly ‘ Se j ° ny’ ess, (aie oe a sy BRS AABMSATASE hl einen Ghe! AYAMSTARA BS Ho www . Bee RIEOTIO 8 Oo ' | : } f ae = a et meee See re Sar: Sea one dpsed xsaortinr tein 1 aRgUDTa cS” ae og ave [amt £ = es wes Be + ae + ihe Abeer! he Ss Ra Se fort 2 f zh y Be ; ch CEL Re os oy ; Hi AO TE ap ae ae F. et eid Toy, = if Ri bs eee { : Ray fe ; : ; F Cae rd d y PRAT, Ay ttn eh a Tet eA. Cooke PARE " ees Gee. | f 2 : ; ite 3 ” a ae iy x i “ ha iG, \ : Spcntes. aes r kw in Ab ¥ nt BL We te fs t ae : a ee 7 4 te : i i nl . 2, oe a HT : a va « K re cate F ao t a b i 4 } > + ; i I ' te ; ) d' j , , ‘ t , , mf AL } . : =) : ea, vent a ma. 1 r ! he ; . r ‘y ' t TU ¢ , ie i ; Lis We any.) a y \ PEL) 2 Us ied rey ah iey = i , F : ) 7 pi +x i ) j RnR ie Pe pass f Sitar hth ae ~ nls Vn oe sh Ri, SE CR TEN PeS, ralsalerms Tie hoy See pat: Dot ek Se eg | bey Ue en LEGEND FIGURE 4 The small amount of mixing at Station "C" is illustrated here. This is to be compared with the large amount of mixing at Station "D" for the same period. DEPTH IN FEET Oo o fe) 100 150 200} * C 28 SEPTEMBER 1949 C 8 OCTOBER I949 250 FIGURE 4 i i aM ry . My ‘, AS ts Nye ay Bas aad gin yi ‘ie nee ry Qee ASBMATIAS 6S Qs ee! Gee) RAHOTOD 8. \ Copies 3 DISTRIBUTION LIST Addresses Chief of Naval Research Navy Department Washington 25, D.C. 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