Annual Review of Fluid Dynamics Vol 1, Goldstein S.

7/26/2019 Annual Review of Fluid Dynamics Vol 1, Goldstein S.

1/29

Annu.Rev.FluidMech.1969.1:129.D

ownloadedfromwww.annualrev

iews.org

Accessprovidedby179.154.162.28on03/01/16.Forpersonaluseo

nly.


2/29

FUD ECHANCS N THE FRST HAF

OF THS CENTURY

B YDNEY OLDEN

Harvad Univesty, Cambge Massachuses

THE R ECDE

he pening decade f he wenieh cenuy wa a peid f pge inuid echanic Muh wa begun ha wa cninue f any yea. Mf he gea dicvee in he ae pa f he peviu cenuy wee bewih u i duing he decade, and he yunge en wee ce fwad. Le u a by iing e f he happening

n 900 and 90 Bnad pubihed decipin f hi expeien nhe cnvecive in f a uid heaed f bew n 90 LeviCiviapubied hi ne n he expain f he eiance f a id bdyhed in a ea f uid by puaig he exience f uface f dicninuiy f veciy, even when he bdy i f unded f wihu hapedge pape n ifing fce in ea f uid by Kua appeaed in90 hi cnained a uin f he w-dienina w f an inviciduid pa a id uface in he hape f a cicua a a ze incidence wihcicuain und he uface and a ne veciy a he aiing edge.

Si Gege Gabie Se wh wa bn in 89 , wa chen a Mae fPebe Cege Cabidge in 90 and died n Febuay , 903

Chapygin 90 dca diein n ga e wih he hdgaphanfain f he equain f eady w-dienina ga w andhe appicain je wa pubihed in 90

n 904 Pand ead hi pape be Figeibewegung bei eheine Ribung he hid neaina Cnge f Maheaiciana Heidebg n he ae yea Ld Kevin pubihed hee pape nWave n wae (wih ne e in ach f he yea 905 and 906) hecaica pape f Sefed and Miche n he hyddynaica hey f

ubicain appeaed in 90 and 905, and Ekan pape On he inuencef e eah ain n cean cue in 905huvi fau if hee cnnecing he if fce wih he ci

cuain uie geneay f he w-ienina w f an invicid uidwa pubihed in w ne in 906 ne in Ruian and ne in Fench n907 and 908 he w f and Sefed n he abiiy f uidin appeaed. Lnchee b Aons wa pubihed in Lndnin 907 and a Gean edin fwe in 909 ea he beginning f 90Chapygin fay enunciaed h e puae ha u f he innie nu bef heeicay pibe w (depening n he agniude f he ciuain pa an aifi pe wih a ha aiing edge he w ha i neae expeien i he ne wih a nie eciy a he aiing edge. nea

Annu.Rev.FluidMech.1969.1:129.

Downloadedfromwww.annualreviews.org

Accessprovidedby179.154.162

.28on03/01/16.Forpersonaluseonly.


3/29

GODSTEI

t bgiig of 1910 Ktta ally pblisd is 190 disstatio, witisios, ad towad t d of 1910 Zkoskii pblisd a ot o tdsig of aifoil stios, lagly dotd to a gapial osttio of tpols

1910 also aylig ad Taylo sowd laly ow dissipati posss mod iit gadits bt lft sap tasitios i sok was igass. Cotosy, mystiatio, ad sitatio w dd. t samya s pt fowad a fo t paadoxs of Stoks ad Witad

Ea pofssioal wok ad sola may d falt wit t itms a os fo my list, bt o wil fail to ogiz t maig ad sigia of tos a ildd o a dy tat it was a fitfl piodt is a itstig gam o ty to gss ow wat a simila list witt i

01 8 wold otai fo t appigs of t st l yas of t sodalf of tis ty, 1901960 Bt paps it is a mo itstigad taily mo isttixis to miat o wat t list fo1900 to 1910 wold a otaid if ompild fty yas ago, i 1918.My mwold a b missig, fo ot oly was agios slowss of ommiatio, bt m of wat is listd was so wad familia tat i t sapd atttio o mly idd disblif o dobt,xpt i t ass of a idiidals t was to b a fw mo yas aft1918w t st wold wa was jst digbfo t w disoisw to bgi to a ti fll t

Fo t sak of oitatio lt s ta a bif gla aad fom t d of1910. t was i 1911, wi ft pliatios i 191, tat Km pblisd is st pap o t otx stt i t wak fo twodimsioalow past a ylid ad t maism of sista. Bad ad sowid of t otx stt i 1908 t ad b mtio of s otis bfo tat by Mallok i 190, by lbo i 190 ad May i 1901(wit potogaps, ad by yolds i 1883 (wi dawigs Mallokpblisd a sod pap i 1910 sbo yolds lid til 191,aylig til 1919, ad Zkoskii til 191.

AYEGH' EVEW F AMB HYDODIS-GENERA EMARK

tid ditio of amb's Hydroynamics of wi t st ditioappad i 18 ad t sod i 189, was pblisd i 106 ad t fotditio i 1916. aylig iwd t fot ditio fo Natue, ad isiw tlls m of t stat of t si ad is wot otatio. omxpts follow

Tat t wok ou ae aea eae a fout eton pea we fo tetd of atatal p B fa t gat pat of t is til bod t

ag of te ook aaae a geneaton ago An te poeent n te te a onpuou a te extenon of te atte M tougt natua go ak to teook n uent ue at age n te ea xte. Wt ae eepto u






4/29

FLID MHAISRST HAL THIS RY 3

as the notable one of Salon's Cni Stins and one o two of ooles books, theywee aid in the extee, with scacey a efeence to the hisoy of the subecteaed, o an indiation to he eade of how he ght pusue his sudy of it

The pogessve deveopent of hs sbec s often an ebaassent to hewite of a text-book of ab eaks that his "wok has ess petensions than

ee o be egaded as a coplee account of he scence wh which t deals Thesubjec has of late atacted inceased atenon in vaous countes, and t hasbecoe coespondingly dicu to do jusice o the gowing teatue Soemeos dea chiey wih questons of matheaca method and so fa ouside thescope of ths book othes though physcay mpoan hady admt o a condensedanalyis; ohes, again, owng o he mupciy of pubicaons may unortunaelyhave been ovelooked And hee is, am afaid, the ineviabe pesona equatonof he auho, whch leads hm o take a geate inteest in soe banches of thesubec than n ohes.

Mos eades will be of opinion tha the autho has held the baance faiy oapoos of exsence heoems ae excded. ome of these though demanded bythe upholdes of atheaca gou te us only what we knew befoe, as Kevinused to say Take fo exampe the exisence of a possibe stationay tempeauewithin a soid when the epeatue at e suface s abtaiy given A physcistfees that nohing can make hs any cleae o moe cetan What s sange sha thee houd be so wide a gap between hs nution and he ines of aguennecessay to sasfy he pue matheatician.

aually a good dea of space is deoed to the moton of a lqud devod ofotaion and o the eacion upon imesed solds When the solids ae faishaped, ths theoy give a easonable appoximaon to wha aualy ou butwhen a eal liquid ows past pojecng angles he oion is entiely deent and

unounaey t e cae of geate paccal impoance The author, followng emholz, as sess upon he negaive pessue demanded at shap coes node to antain what ay be called te eecic chaace of ow. Ths explanaion ay be adequate in some cases but it is now we known that liquids aeapable of susainng negaive pessues of seveal aosphees How too does theexpanaon appy to gases, which fom es unde quie ow pessue dieences? seems pobabe hat vscosy mus be appld to. Ths a mae whch muchneeds futhe elucidation It is one on which evin and okes hed stonglyd iegent ews .

It woud no have accoded wth the authos schee to go into deai uponexpemenal mates, but one feels that thee is oom fo a suppleenay volumewhch shoud have egad moe especay to the pacca sde of he subect. ehaps he tme fo hs has not yet coe ung the ast few yeas much wo hasbeen done n connexon wh aca igh. We may hope tha befoe ong thsmay be coodnated and bough no close eaton wh theoetcal hydodynamcs. In the eanime one can hadly deny hat uch of the lae science s outof touch wih ealty.

ayligs viw is a ma ably itstig vw ad sot ssay octio wit m y 900 to 90 list ad t mak witt wit t bt of idsigt tat m i t list was so w ad familia tat it

sapd attenton o me e nded dslif o dot givs a illmiat ig pict of t gal stat of aas i t ic i 96

Annu

.Rev.FluidMech.1969.1:129.


Accessprovidedby179.154.162.28on03/01/16.Forpersonaluse

only.


5/29

4 OLDSEIN

Lamb' ttbook wa th pdomat "high-ca ttbook o mayya ctaiy i Egad th 90 fo tudt of appid mathmatcbut w w ot ay happy wth t aygh may ha cotatd it wthth aid ttbook of th 860 but i th 90 w w compaigthat t wa mpoib to mmb whi adig Lamb tat wat w

omthig of th am dy atmoph ti pit.By th d o th t hactuy th wa a tog ad mo wid

pad mt o phyic i thought ad ach o ud mchac thai th t twty o thity ya a thi mu ch mo o by ow Safacto ad a ach wok cotibutd to th but th gatt iuc ha b th amp of . ayo

Fuid mchaic i a pat o appd mathmatc o phyc o maybach of gig ctaiy ci mchaica chmca ad aoautica giig ad of aa achitctu ad gophyic wih atophyc

ad bioogica ad phyioogica ud dyamic to b addd. Sgicatcotibuto to th thoy of afo cam ay i th ctuy ad dugth who of th t af of th ctuy appid aodyamic wa to bpobaby th mao ict daig wih qutio that w mpotatao i mchaca ad cii giig but gophyica quto ctayot without cham ad aciato id much atttio.

Cuioity about at a two of th bach o uid mchac ad thiappicatio ha a og ad ditguhd htoy fo i th ob oSoomo th o o Daid kg of a t wa tatd th wod of guth o of akh that h b th thg which a too wodu o

m ya ou whch kow ot of whch two w "Th way of a ag th ai ad Th way of a hip i th mdt o th a which tak tob utio o aodyamic ad aa achtctu quto that co

h ow o dath of book om y good ad may atifactoyo th aiou bach of ou cic i whch th dtai of th wok doup to 90 may b ad. So popo ot to attmpt to b ytmatc o to dicu a igicat advac but to pad i Lamb' wodth iitab poa quatio of th autho which ad him to tak a

gat itt i om bach of th ubct tha i oth. Lt u goback to 1900.

T N FU. T UDNNUY TY

obaby th outtadg dicuty wa ti that o accoutg o thitac of a oid body i motio ati to a ud i whch it i immdh th kow tho w ot atiactoy though th wa t coidab dc o opo about th at o tm ccodig to th daof aac wto th foc o a at pat a two-dmioa moto woudb whoy oma to th pat ad popotioa to th qua o th of

th ag o icdc i. th ag btw th ati ocity o ud

Annu




only.


6/29

FLUID MEHAI-FT HAF OF TH ETY 5

ad soid ad t ta of t pat at it was d tat i a iisidiid, ba of t toms of agag ad Ki, a mtio satdfom st woud b iotatioa, a t woud b o fo o aisoatd body moig a a suit dita fom ay boudais w tmotio is stady, t i of t motio of t id big ompty

aod fo by a modiaio of th itia of t soid T t toy iod sufas of diotiuity of tagtia oity bgiig at sapo, ad i patia fom t dg of a at pat i a stam. ambwits (pp. 64 642 of t ft ditio of Hdrodnmc 924):

a a, , a to a w a aadx db xa a , a p a x ai a ad a a waf b t a pa aa. b ta

m a d b aa, a a t bg a o a tx.

ayigs 6 pap " sita of Fuids bgi y obigtat "t is o pat f ydodyami mo pxig to tdtta tat wi tats of t sista of ids. ambs paagap t"sista of Fids bgis by obsig tat:

b a a a aia , p p, pi, ad wd . a b d w wd wig bai pb

f aa t kwd i i a pa."sista was a tm usd fo th tota fo, ot t dag fo,

wi was "t sod pat of t sita i t diio of t stam is itsig tat ayig ompad, i at, t s of yfo a at pa at ags of iid btw 0 ad 90 wit masmtsby Vi pubisd i t Phloophcl Trncon of he Rol Soce i9. Vi ad masd t "dag, ad ayig diidd t masudsuts by t si of t ag of iid to obtai t "sita adompad t atios of t sista at a ag of iid of 90 o t

sista at oth as () do to 0 t mad t f is xpis ag w o aab w ad

a wi i i ia w f ot xi w ad w awiig ai ad aa t a b af dd; w o a a a b aa. w b wiadaa

ow th toy was by o mas wiig ompt apta. patiua Si Wiiam omso at od Ki, was i oidayig wo:

wa b a i aw a a

Annu.Rev.FluidMech.1969.1:129.Downloadedfromwww.annualre

views.org

A

ccessprovidedby179.154.162.28on03/01/16.Forpersonaluse

only.


7/29

6 GOLTEI

fa of aatio a tab i i o dobt t a t it ma bdobtd wt t allato of ta a mata atd b t mta a t xd mt b aly iddt of wat a at om dta t a of t obtal, w t tabt wod tb to maift itlf. . foma ood i t t a a alo

labl to a ta amot of modato fom fto w t wold b dtto timat bfoad, bt w aot b odabl f t ximtof i a to b at all ld o

li m to a b mo ad mo oid 89 blid fo ot o t qtio of ita i Nature wi a odd i Volm of i M P P, it a ot byt dito, i o amo, tat T ommiatio fomd t bj t of a ologd layfl otoy btw od li ad i itimatfid i Gog tok, i a i of ltt i a b dli owd tat t lt of t faofdiotiity toy fo aat lat ot i agmt it t imt of Di, blid it Proceeding o the Royal Society i 890. T dito of t Mathematicaland Phyical Paper qid fom t Dito of t atioal yialaboatoy, D T E. tato, abot t liability of Di lt adabot t lt of mo t itigatio, bfo bliig lia i 1910 tato ot tat w alloa a mad fo di i iz of lat, Di lt omad wll it mo t mamt at t atioal Pial Laboatoy, ad tat t x i ttotal ita o tat gi by od aylig fomla a d to t

tio t o t ddi o t lwad idiCiita t ot o t xtio of t faof-diotiitytoy to ow at olid bodi i d bodai, fo wi ottat gati d ot t, wa blid i 90 ad t ga matmatia toy followd 0 H ogt to tify t matmatial itigatio by t o of atial omaio, fo xamlto i, bt alo by omaio wit blid ximtal lt. t iittig tat t obatio to wi fd (by May ad bylbo a amog to i a alady b mtiod a owigid of oti i t ak. iCiita i fat makd tat i tatal wak t a otial ad tblt motio, ad tat at a taidita fom t body t tat of motio of t id o log t aytig of diotiiy, bt agd tat t ita dd oly o ttat of motio i t a at of wak i otat it t body, adtat ti tat of motio i tbly t am i bot t atal wak adi yottial o o t al of t ita ltig fom i allatio old loly aoximat t ot al, i it of t dff bt t atal imta ad t totial modl (Tia tially aylig 876 agmt bt Li-Ciita diio i

log ad mo dtaild all ot di t aliatio ad ft

Annu




only.


8/29

FLUD MECHANC-F HALF OF H CENUY

dvpm Lviivias mhd by isi ad Via ad a byhs xp mak ha h mahmais was bh sidabaayia diuy ad is ad as ha a uvd buday hsui is uiu ui h psiis spaai h samish as h suas disiuiyhav b dmid

ad ha his h is y u amy ha i may b uid hah uvau h samis a spaai pis shud b isi ga psiis hs pis his uvau is ii. Wh iis i i is ua h uvau h si h sid buday

Th was h i h s pa his uy sm usi abuh vaidiy h suas-disiuiy hy h appximaauai sisa. Whav i did hwv i idud hi ampig big h sus h pia hy h mi ivisid uids i b agm wih bsvai i uids sma

vissiy by h idui disiuiis i h viy d i hisas vxhs whih was pv a vauab idaizai i spi isabiiis O us i xisd as sidab mahmaia asiai ad i Egad a ay a i was aways ad ah xsivyby suds appid mahmais. d kw hw muh im i ayis sp i w Th is si muh b said ahig i bu i ha isd hp i is d w as i was d ai wih a u dsipi h aua iumsas ad disssis is ais budayay spaai ad h isabiiy vxshs ad ays

BUNY NN. supps ha i is si ha paia pupss i ms siua

is u uaiaiv kwdg sisa i maiy mpiia Hwvmuh m s udsd w h udyig physia psss ad wmay ask wha was h mai aus h diuis ad usi aiy dd i i ay ak iua abiy vy disiguishdsiiss w wsd wih h pbms m w ks adayigh Th a ub was dub abu h buday diis bappid a h dividig sua bw a sid ad a iuid gas. h

hy iaia mi a ivisid uid h aiv maviy a h sua a impmab sid mus b z ad hbuday dii is uid a b impsd h mi avisus uid h h had adig h dyamia diiauais pbishd duig h pid 18 185 avi 18 iss189; aiVa 183 ks 18), ah buday dii is uid a sui. h was dub ad vaiai a g im. O hwh hg sms hav b agd ha h s sip i.. aiv agia viy a h sua a sid bdy i h as avy sw mi i a vius uid bu a s was i dub. h

hyphss ad bis ig h diis a h sua bw a


views.org

A


only.


9/29

GODTEN

ud ad a olid od i pied a a appedi a e ed o e eodvolume o Modern Developmen n Flud Dynamc ad a a ieee ill o e epeaed Te diepae eee e aual moio oa eal uid o mall vioi e lamia ad e eul alulaed oe ioaioal moio o a iviid uid aie mail i mo ae ome odiio i a eal uid o o lip a a ouda a uid ould lipeel ove e uae o a olid od i ould e a ve die oldToe amog em Lam ad Leviivia o ave aeed i e paa vioi ao e oideed a edomia aue o die eiaeee oe i i ee i mo odia iumae

i 904 eue o e eaioal Coge o aemaiiaadl aed ie u deiel a a e mo impoa queioi e polem o e o o a uid o mall vioi pa a olid od ie eavio o e uid a e all o e olid od He oiued (e

oigial Gema a ee alaed T pc pc t bu Gzcct) btw ui

i b c b ccut i uct tict w t um ttt u t t w, tt t tt vct t z qu ot vcit t b e vct v m t pt t u gt w t t g, t vct w v g t uu vu v t tw. t ti tti (bggcct) t p cg o vcit pt t m vct cct, puc tcb ct

92, i e oo o e eoeial ae o aeoaui i i ileue ee epodued Zuovii poied ou a o a iompeile

uid i a uiom oeie o vioi e em i e dieeialequaio o moio oaiig e oeie o vioi diappea o poeial moio o e iuee o voi e a poeial o e veloiei a appea ol a e all ee e ouda odiio mu eaied He e emaed a ae a a ee ae dieig opiioo e evio o e oig uid a e all ome iveigao ougee a o moio o e uid alog e all ile oe uppoed ae uid lip alog em Fo i pa e oug (ee a o ea epeimeal omaio u i appoimaed eal eoug o eali) a

e uid veloi i eo a e all ad apidl ieae uil i eomeequal o e eoeial veloi e lae o uid aoud e all eigvoial ad alo ve i

e ed o e ieee eu e mo aiao eoeialpoge oe a maemaial ad ee made i ae ee e ouda odiio a a olid ouda did o geal ae e eul a oave o ae o o e oe c ee e odiio o eo lip a aeped lo moio i a viou ud o e eo o Soe o a peead alo o a ellipoid ad eai polem o mall oillaio Foave o ae meio ma e made o e ee o a loal diuae

(oio 8 au 827 Kelvi 887) e eo o goup veloi

Annu




only.


10/29

FLID MHAISFRST HALF F THIS TRY 9

So in an xaminaion qion, Smth' Prze Exmnon, 187Rayi, 1881 Obon Rynod, 877), and o apiaiy and minim m wav-voiy Kvin 18 71 ). On i b m o a po a bn mad omwa ny.

FT o oy o ow o iniid id wio voiiy w

widy a vaian wi obvaion pai o mo o impoanpa o voiy d o ow pa b bodi, ba ondion oo ip a a o id a wa no aid Howv, oy wa o poi wo o ai-apd amnd bodi a aioi, na, andaiip, o impovmn w o b diab o paia appiaion a aaion B a i ano oy, wi wi bmniond a. am xin o oiiy in a did om

and a n vioiy, moion o a oid body in a id poin voiiy i amnab o aaion ony in a w a On a i moion in a niomy rog id In a i o pap oni b bwn 1917 and 1923, G Tayo mad ain oiapdiion and pod ain xpimn o a in and impoan, no ony o m and i appiaion b ba pdiion w mad a i did no dpnd on bonday ondiion oa a no ip a a bonday. T pdiion w id by xpimn In i pap on xpmn wi Roain Fid in 1921 G Tayo wo

we ow preo ou u oo e o e ro eor re eo ere expere perfore w uu. e expo of w o greee ewee eor expere o e fou e e oo e urfe of e o oure of eu

Te ro eor ue perfe ppg e pewere u u e urfe er of e u re ure up o eeI e e of oo w epe o e oo e urfe erefore ogreee o e expee ewee eor expere T o uoo uforue ue e were a o oe roug u w

orwe re. e oer ere re pe of u oo w o epe o a eon exe o ip a bondi. Fo i aon oa preoou we e or ou e moo of orex rg re u eergreee w oero preo ou e oo of o u.Soe e go e pree wrer e er preo ou e oo ofo rog u or rer o e eree w g e expeeewee e oo of o rog u oe u re Te pree feure of e oo o epe o oo e oure w erefore o e pe e g e ere expere. Teexperme were rre ou e preo were opee ere

I ew of e ere w e o expere ero of e

Annu




only.


11/29

GOLDSTEIN

ru mi r prur i rig h mi f i ui m wrh wh t pubh phtgrp wg h xprim i prgr In h thr pr o isppr urhr xprimt r rb whih hr priti r ri rm w war

am papr oaid a poo y oidraio o irlaiorod a iri a i ay mal moo i ommiad o a id wii iiially roai adiy i a oid body rli ow m b wodimioal o mal oiaio abo i a o ow moio apobl w a tnt tht praiay am i a a prioly od by Prod ma a ma ady moio o a roaiid ar wo-dimioal T papr o w rmar a I a rpapr aor op o di wa app i a w bodari o id mo owy i a way a dimioa moio

m a plaMor wa o olow rom aylor iml ad m m mor

rom may or Moio i roai id pary b o rly oropyialmoooial ad oaorapiappliaio a boma ar ba o o id dyami T xpim rprdid ad obrd by aylor ar rii i rm b y aow adqaly dbd lwr or w rr dopmi bj m b abadod r or a rr o mar prioyirodd

BN L BNL NVX N

Pradl rmar i i 1904 r o Iraoa Co oahaas o bodary oio o n ip ad rmai a i ayr o id ar a oid wa a arady b id. rwa rprd i 927 a boo Vier Abhandlungn zur Hydodynamik unddnamk, or wi Prad' wo ai papr o 1918 ad 19 19 oairoil ory ad Bz papr o 1919 o rw proplr wi miimmry o. I i boo papr o moio o a id o ry mall

ioiy opi l a i pa. M o r wa dod owi o ambld mamaiia qaliai diaram o amli ad paraio o ow pa a ro orr ad a ira yidr w roli p o orx ad xprimaly obadpoorap o aa ow i imilar a wi bodaryayr paraio w b- tn. v rad n tm tdri r a i a rio o od ram wr oriiy adb prodd by aio o a mal oy or a ry o im voriiy wold b oa a o-dimioal ow ad o aoa i wold b proporioal o da rom ai o ymmry or

a aymri ow o bodary-ay qaio o ady wo






12/29

FLUD MEHASFS HALF OF HS EUY 11

dmnonal ow ; o mnon dly o nmal ompaon anrom nla a wall o a orm o mlar olon oow alon a a pla, a ro opaon o da an od bondarylayr paraon n pn o a pr nan n ram dron, w a daam w a bn rprodd v n

Pandl wro rman a b ranlad) : mt imptat ut t ivtiati r appicati i tat it

ca t ui w wi paat m t wa at a pac cmpt tmib t ta citi. A a ui, wic a b t i tati b titi at t wa, ma it wa i t ui w, caui a cmpttamati i t mti it pa t am pat a a Hmtz uac iouit vo ald o vora i at (it i pptia t (k/u but vti mai ua o a o a o w o o l = a obai alway tam w pictu . . . .

Prandl pland plabl raon or paraon w an navoablp adn, and pland a ondaon o a ow m bdal w n wo nran pa, an nvd ow obyn Hlmol vo om, and anon ay bonday layr) a old bondar n w moon wl b rlad by d b w v r ram ara by mo o vor layr

wa a mo raordnary papr o l an pa. In 928 Iad Prandl wy ad p o o, and rpld a ad bvn n mn or lr a Conr and a, bn ll q

youg h ha hough h o h oy ha h a ha o sa papr wll ranly prov o b o o mo raordnary papr o nry, and probably o many nr O or, o a lmd n n and nar o a bondary lay and onnon w ronal dra ad bn by mnon bor Rann, 84 Fod, 874Mndlyv, 880, b ad amond o vry ll ompard wPandl onrbon r wr no bondarylay qaon and noplanaon o paraon n o Prandl bondaylayr orya bn nomo. I a bn d o ma la pyal pnomna aw, o wold av bn, orw ban or a la my I ormd ba or appoma mod o ompaon o praal ly daw appld o n o an d dynam and, n d dynam, aon or an o nvolvn a mall voy Ar onlono al-ny wa ndd and nrald nd ranmd, pally by Kapln, Larom, and r oworr, no ory onlar prbaon or approma aympo olon o drnal qaon.

Howvr, or om ya a wa pbld Prandl l waalmo, no omplly, nnod. Prap no pn I wa

o vy or, and wa pbl d wr no on wo wa lly o apa

Annu




only.


13/29

1 E

be expee . In 9 la pble n a e aebe e nvennal e nan a l e an eean e bnalaye ean an a eale nean ew aln a a plae paallel a ea b even ae a ee wa nealy a aepane expn e nvean bndaylaye ey. la al bean e y e bnay laye a eae a a ylnde aed o e le n a nen en 19 ed bnay laye a e ae be evlnepeally pee and n 1911 Heen peed bndaylaye pan w an epeenally eene pee dbn n aa ynde. ee al dew l aenn

anee Adnamcs a ben pble n 197 In an ee e n ndependeny a e n da wd vaya /U3 ave an explanan epaan le ealed an Pand

ave ndan a e new ab blene n a bnday laye expaned a a eane bdy ne a n n a de n ve e a ae nny an expee epaan be delayd n ne de and aened n e e de a an ynden a ea. T pban peably dew even le aenn.

W e pban n 1921 Kn en ean an enPaen appxae e nean and e pban n 1924 e expeen . M e and van e Hee Zjnenbndaylaye ey a a beae e be e aenn andaepane.

Te ne eeene Pand bndayaye ey n ab Hdr-dnamis n 1924 e) neen ab ea a n w paa yne

the cntral stam-line dvds whr t ets th sufc n ont, nd then

ws e surace r sme dsance n ec side e mn e ud n eeran beng farly m an regular. A a ceran sage wever e sream-lnen quesn appears eave e surace and can n nge be eney race e

sace beween s apparen cnnuan an e cylnder beng lled w ees.An able aemp race s penmenn maemacally as been mae byPran. Te regn n frn f e s s regare as mae up f w prns vz

(1) a n sraum n cnac w e s w a rap varan reave(angena) velcy n e recn e ckness an 2 an uer regn n

wc e mn s aken be rraal beng praccaly unaeced by vscsy Apprxmae sluns e eqao f mn are sug apprprae ese w regns an cnnuus w ne aner a e cmmn bundary Tealaon ae eea eaboae b e e w ae epeenedgrapcally are neresng.

Tee ae eeene Pand' le and aTe an wa aee appeably n e en Hdr

dnams pbe n 1932. T naned a new en n bnayayeey w eeene Panl a la a bee and Me






14/29

LUD MECHANIC-IR HAL O HI CENUR 13

ttmnt n 92, n t mb n ntbtn t tKrmnPolaun pproxma mod.

n la 192 and arly 193 r wa arn o u and udyboundarylayr ory o wa appropra o prn a moo oModn Dvopmnts in Fid Dnamics an xra rom ay o rFran Baon 12 For wn propoon ar n r an ndo m bu y b allowd rqur a nw wor.

W u ndrandn o boundarylayr paraon oupld w nowldtht n mtn o old body ard rom t t ud t bto ma nal moon rroaonal wou rulaon w a orx wrappd round ura o old body and alo w omundrandn o rolln-up o orx way wa lar orondrabl n no mu a wa no lar bor orn o alar t t tn t vt mtn bhn a blu

obal and orn o rulaon round a ln arol.Krmn pond o a a oral drmnaon o loy

and pan o or n orx r would rqur an nano pro o orx ormaon and rrrd o Prandl ory o moon o d w mall oy or an xplanaon o ormaon oor n n a ud o annly mall oy.

n 92 uo ad ondrd ormaon o or Tr wat th bm th ngty n th tn t ng g o anarol o ro n u a a rular-ar arol uo bldt mply t a vt tnng. Ktt thght adurban arn rom ladn d would no b mporan. ornrally r wa armn on drably o a roundd no andr do no appar o a bn any wdprad unan n orand uo pond ou a or ould alo para rom raln d and ou a man au o all ran o b oundn u paraon.

anwl n 19 da abou ran ad bn lard n rporby Ktt ar Fnrwaldr and by Prandl ml. Fnrwaldrn a lur aually dlrd prou yar ad dud Prandl

ory and mnond dul bu pond ou a rom ory b ddud tt n t o n h t nt mu orm o no a mar a ap o al Prandl nrodud da o dra bn du t t au w ar no ndpndn o on anorn r o ura ran ron and orx or orm draC . anon rply o Larmor n onnon w publaon o Klnpapr nt ad aly a t m th t t o a body a nmany a mor mporan or dra an orward par. By uablyormn ar par dra o an arp ull ould b rdud o a

am ar o tht alu o ro Prandl onnud tht all ora ry o ba dra on wa appn n ron mu lad o wron


views.org

A


only.


15/29

4 E

et, nd mut be eeted oeoe, e y, te gete o e tbene of te of get mpotne fo te vue of te dg.

Te onen wt te degn of t tt tme motn.Ao notewoty te efeene to tbene, w w be mentoned te

Et, o even oug, to, wee not pobe nd te woeoe w not ometey undetod, bt ome tme te te teoybegn to ve ondebe nene on degn In ft by te te 92 ndey 9 temnng w fonbe wod, even f te ometeymundetood by nonpofeon. Mny tng, no mtte wt tee n eton to te ten menng of te tem wee efeed to temnedfo eme, ft moto , ft od tn, nd, odn g to dvete, geebe young women t ny eed f equed wt tegt foundton Te ng e of te tem ded out, pty e oooog eo, bt ty ep beue of te dte of

9 to 9, but te t, ene, nd tenoogy of temnng n t ten menng emned of pm mpotne, t ny te unt eneton tted to beome engneeng ft.

Te noton of t-o vote, wt vote beng fomed nd detedn ot tme wen temned) fo t ft begn to move, o tt uton ound te fo n n opot ene eft, gve py ubtne to te ton teoy o t. Mny tkng epement ve beenmde n d men nd eodynm, nd t noton of te tovote ed to one of tem ve neve fogotten wen m Fenowed me, on m e mode n tnk wt tnpent w, teto vote wen n fo w tted nd ten toped mveynd te vote wt oppote otton ppeed dy, nd movededtey downwd eendy o te ne onng tem, n odac w o. ing wa il bvng. detonof te tnk, et, nd te epement eed n ke te (92)

ROL THEOR

Te ton teoy o ft w not wdey eted wt ny dtyn te ey 92 t et one dned eont engnee w t

eeng etm, w oded t eement of ynt & m(92) t te ton Py Lotoy. T not ony veed teetene of uton bt onmed te Kttkovk fom foe ft, even fo e ud wt te eene of wke, f te ontoound w te uton tken doe not ppo te fo too d t te tg wke t gt ge to deto of t dtbed etve moton. e obem w ten not to epn te ft, btto en y fom w o ney oet n e peene o owke, nd t epnton w mmedtey ovded by G 1 Tyo.

Tee e tee ngedent n nvd, nompebe two-dmenon

fo teo te ft fom, te ondton t te tng ede, nd te






16/29

FUD MECHANCFR HAF F H CENUR 1

cnfrm mpping f he irfi cntur. As time wen n the secnd wsimprved by wnces fr the budry yers nd the wke. Tw-dimensin irfi thery ws etended by Mises nd by Krmn & Tretz mngthers . t is ntewrthy tht the thery f the cmpe vribe ws incres

ingy used fr design f curse with the desired physic, mechnic, ndgemetric criteri in mind), cumiting in the wrk f Lighthi 194The methd f singurities ws s deveped fr ppictin t irfisectins

Prndts tw cssic ppers n three-dimensin irfi thery werepubished in 1918 nd 1919 eding ccutins fr irfis f rge butnite spec rti. Thee ppers hd been sever yers in the mking, theides dting bk in prt t est t 191 with the rst pubished reference inpubictins by pp in 1911 pp s referred t Lnchesters Ardynmic in cnnectin with pir f triing vrtices which strt frm the

wing tips nd mke pssibe in simpycnnected spce, the trnsitin frmw rund the wing) Prndts ppers re cssic, nt ny fr erdynmic but s prt f uid dynmics genery. Mrever, I remember thtwhen I rs red them I frmed the strng mpressn frm the wy theywere written tht Prndt rey knew he ws writing cssic ppers

Much reserch ws ging n bth befre nd immeditey fter thepubictin f the tw ppers mentined bve, nd nything ike fudescriptin is nt pssibe here. The term induced drg ppers t be duet Mun k 1 9 18 wh s prvided wht is nw knwn s Munks stggertherem mentined s in Prndt's secnd pper) nd n esier nd mregner prf with generiztins tht wings with eiptic ding hve thesmest pssibe induced drg. et's pper n the screw-prpeer withest energy ss ppered in 1919 Tretz's methd f wrking in theTretz pne nd s f using Furier series ppered in 1921

The rst prctic triumph f the thery ws in mking sense f eperiment resuts n irfis f vrius dierent spect rtis

The news f Prndt's irfi thery spred much mre rpidy thnthe news f his bundry-yer thery n 1921 the tin AdvisryCmmittee fr Aernutics in the S.A requested nd pubished reprt

by Prndt himsef n Appictins f mdern hydrdynmics t ernutics, nd in the sme yer Pistesi drew ttentin t the thery in ecture nd pubictin in Ity. The sme uthr pubished mre cmpeteepsitin in the fwing yer As in 1922 y pubished bket n thethery in Frnce nd in 1923 the thery ws epined nd used by Guernd by Lw, nd veried eperimenty by ge & in, in Engnd. AGermn tetbk by uchs & Hpf ppered in 1922 nd Guerts tet nTh Emn f Arfi nd Arcrw hry ppered in ngnd in 1926nd rpidy cme int very gener use

A ppris f the cntributins f Lnchester nd their inuence

wud requie t est cmpete rtie Durnd, in his Histric sketch f

Annu.Rev.FluidMech.1969.1:129

.Downloadedfromwww.annualreviews.org

Accessprovidedby179.154.162.28on03/01/16.Forpersonalus

eonly.


17/29

6 OLDSEN

dvopmn o arodynami ory po o Lanr rmarabpya ini and o i r i no doub Lanr rad a papr o Birminam aura Hiory and ioopia Soy in 1 894 n arvid vrion o papr o a ow or pbiaion by Roya Soiy

abo wo yar ar and wa rar rioy advid o nd o yia Soy wo rd n Spmb 1897. Aa om ain oa pan Lanr mad no urr or a pubaion n Aodynamicswa bid in 19 and Aodonic in 198 Hi r onribion o ory o win o ni pan and arrw wr pubid in Pocdings o h Insiuion o A uomob ngins in 191 and rprnd a aboo A rman diion o Aodynamics wa pubd in 199 and an diion in 914 bu pubiaion o 191 rmaind ary unnown n oninna Erop or om im and Prand ad a didno bom awar o m ni 6

A a ry ary a in a a anr ad ndamna dao raion ory o i and o raiin vor bind an aroi on pan Som anion wa oon pad in Erop o win or nAodynams In 191 Zovi rd a Lan' a mwa in avin imnad aa rom an aroi o inn pan orwi d opid by id i dobyonnd o ni winor w d i mpyonnd Fpp' rrn in 1911 a aady bn mniond. Howvr no anon wa pad n mu ar oanr' ori in i naiv Enand Hi wor onaind bu i

mamaia dvopmn vn o apood in pra oAodynamics o non mamaia radr wo may nd im ou o dp or mama a wa nudd. Lar n i WburWri ur ad a wrn wr in pain Eni divd oa mamaia ornam bu in a pain ni or no y wr byno man ay o ndrand. Aodynamics oud b rad no ony or onn bu o aor Lanr' y Many word d wr i ownoina and or wr d wi wa i now an obo mann o aoary i ndd and n a prvidd in boo For xamp o 894 par o Brmnam ara Hory and Pioopa

Soiy wa Sabiiy o an aorom Aodom wa apparnyLany' word i wa d or a yn main T Oxod UnivsaDiciony ay a word wi manin o an aropan da rom1891 and bam obo n 8 w m rar ard on Lanwo d wod in a n vry rmy n Aodynamics in 07. In ain a oono wro a word rodrom a bn roy miappidby oninna wrr o dno a baoon d Random Hous CgDicionay ay a word airdro in nid Sa) now man anarpor o an o manin in wa wa ad abiy o anarodrom m b nd. onn o ary par and vradaram rom i wr rprodd n Aodynamics.






18/29

FLD ECANCFR AF O CENRY 1 7

core eveny enon w pd o Lncee conronn Engnd nd e w nved y e Roy Aeonc Socey o devee r g emor ece n 126 ye eoe Prnd

Pnd ece e egnnng o c e ed ime w dn

compeed y o ow nce Pnd d oe w e Engngge w on e geneon o voce n d o m vcoyy e con o e ondy yer o on ro eory ece e de og wod e preere o eec noer ec w wc yore poy e m n ngnd og egnnng go e cn do oe o e eroo eoy oweve er eeng o ode ndng ncee devoed n pprome eoy or edymn ow n connecon w ondry ye rnd oe rey one oy o o eoy He d

n Engand you refer to t as "the LahesterPrandtl theory and ute ghtlyso beause nhester obtaned ndendently an mortant at of the resultse ommened orkng on the subjet before I dd and ths no doubt led eole tobelee that anhester's nestgatons as set out n 17 n hs erodynms'led me to the deas uon hh the arool theory as based But ths as not thease. The nessary ideas upo whch to buld up tha theory, so far as these deasare omrsed n Lanhester's book had already ourred to me before sa thebook n suort o that statement d e o ont out as a mtte o at wen ermany ere better able to understand anhester's boo hen t aearedthan you n Engand Engsh sent men ndeed hae been reroahed fo thefat that they ad no attenton to the theores exounded by ther on ountry

man hereas the ermans studed them losely a d dd d therefom. he truth of the matter heer s that anhester's treatment sdult to folo sne makes a ery geat demand on the readers ntute eretons and only beause e had bee orng on smlar lnes ere e able ogas Lanhesters meanng at one. At the same tme hoeer sh t to bedstty destood tha mny paua espes Lnhese oked on dfeent lnes than e dd lnes hh ee ne to us and that e ere thereforeae to daw many se deas om hs ook. The voume pshed n 5 . . nhh anhester omes to the same onuson th regard to the ndued drag we dd w nnown o n 2. As apen the same fomua w u

lshed by us n 11 by Bet) . . emn o dd e voeee mode o Lncee nd Pnd

fomed o e ng on o con on ngrce eory owc mc enon w pd n e nd nd on wc wo oceedng. In 16 Prnd nodced e cceeron poen nddcd dwnwa ga o n wc an ov wngce ony. Spec pnorm n pcr epc nd crcr pnormwee condeed y Knne ) y Kocn 4 nd by Kene14) nd perp moe mpony, nmec meod cme more nd

moe no ePand wn pnan wa cpy na

Annu




only.


19/29

8 LDTE

insighs n i hs lely been poie o eg in nompib odynmi eie by Thwies (1960) n in Khemnn's "wig nlemol ee (96)] h wh n himself lle lifing-lineheoy ms be onsiee n ppoime lifingsfe heoy in whih

he howise isnes involve e smll ompe wh he spnwiseisnes n sh se i n be pove h he ho wise oing is hesme s in he woimensionl se n he spn wise isibion of lif isgiven by n's lifing-ine heoy

The ime me when he inene of he ompessibiliy of i highsbsoni spees o no be ignoe, n so heoei onsieions ofspesoni igh wee ken moe n moe seiosy Swep wings h o beonsiee ppes h he s pblishe sggesion of he se f swepwings ws me y ez in 190 Sene i beme mes of seiosonsieion only onsieby le b heoy of poine wings of veysmll spe ioin onisinion o he heoy fo lge spe iosws pblishe by R. T Jones in 196. n ll ses iing voies wee siwih s

SY

Among ohe mes eiing he iosiy n enion of invesigospobly he mos impon wee sbiiy blene n gs ynmis

Theoei invesigions of sbiy in he peio el miny wihsbiiy o inniesiml isnes on ineize heoy ogess in

onsieing nie isbnes ws no o ome nil len 1916 Ryleigh onsiee, s qesion of sbiy, he onveionens in hoizon lye of i hee beow, in onneion wihobsevions of n in 900 n 90, menione in he 900 o 90 is e eginning o is ie yeigs isssion is se on e ppoime eqions of ossinesq e emke h n i noppe o be qine wih ppe by Jmes Thomson in he Podinof h Gow Phioohi Soiy fo 11-12, whee ike se wsesie in mh hike lyes of sopy we ooing fom he sfe nhe Sini Pp hee ppes oe e in 191 bo his own wok

h "This poblem h ley bee ee by Aihi (Po Tokio Mhh. So 190)" The pobem ws le onsiee by Jeeys, owellew & Sohwell n ohes Ho Jeeys se o ll i he "poigpoblem fo obvios esons n iion o he onsieion of nieisbnes, ohe fos wee o be e sh s he inene of sension n is viion wih empee b hee ws nohing boyeigh's sbliy pobem h so be e onovesy n henvesigions o be one s eniey sessfl

n 19 . Tylo pblishe his lssil ppe on he Sbiiy of

visos liqi onine beween wo oing yines The esls of heheoy wee enie n oe, in geemen wih he epeimen e






20/29

UID MECHANICSIRST HA THIS CENTR 19

us. implcains he mahemaics sucen r he reuired pupses and many urher cnsiderains he w beween raing cylindersee lw bu hee cud be n nves.

ereys demnsraed in 92 he mahemaical equivalence he w

sabiliy prblems cnvecin and w beween raing cylinders aneuivalence which had been suggesed by Taylr and LwThe ind insabiliy hreedimensinal disurbanes r w ver

cncave curved suraces exemplied by he wr Taylr in 922 and laerwr n he ransiin urbulence r w beween raing cylinders wasnce a cause r sme cncern in airi desin. Once pn a ime in cnnecin wih he design lw-drag suin wings r which he bundary layershuld say amnar as lng as pssbe a he ana hysca abrarywe designed an airil secin wih a single sl n each surace and wihavrabe pressure gradens eerywhere ecep a he sl. Te w wasdne by Richards mdel was made and esed in a wind unnel n spie he avrable velciy gradien behnd he sl he w in e bundarylayer became urbulen sn aer he sl ecep a lw Reynlds numbersThe airil srace was cncave he w a he sl and e ransiin ubulence was undubedly cnneced wih he hree-dmensinal insabiliy in w ver such a surace and is urher develpmen rbundarylayer w his insabiliy was sudied hereically by rler in90 bu because he war we did n nw rlers paper alhugh inac rececin Tayr's wr n he w beween raing cyinders

hl h n nuh Transiin urbulence in he bundary layrn a cncae surace was shrly aewards sudied eperienally byLiepmann 93 whse resuls we were inrmed. s we said a heime all he laws naure always cninue wr including hse werge

s regards he denieness hereical discussins prblems sabiliy he sae aairs was dieren when i invlved discussin herrSmmereld euain r paralle ws. Much cnrversy develpedaer Heisenbergs discussin in 192 he sabiliy pane Piseuie wwhich did n die dwn unil C. C. Lin claried he general hery and gave adeaed cacuan he neural curve.

Doubt and conroversy had appeaed ee 9. I 9 Raleihdiscussing wr by Mises and p n he appareny simpler prblem plane Cuee w had remared ha Dubless he reasning emplyedwas sucien r he wriers heselves bu he saemens i pu rwardhardly carry cnvicin he mere reader. The prblem is indeed ne nrdinary diculy

There were even mre causes r dub and cnrversy ver he calculains by Tllmein he sabiliy he w in a bundary layer n a a

pae whu a pressure gradien lwing pevius discussin by Pand92) and iejens [922 hesis and 925 and hemselves wed by


views.org

A


only.


21/29

0 S

frher aaons by Shhng (1933 and 1935) Fow n a bondaryayer s no reay a parae shearng ow as assed n he aaons oreover, for soe e eperena observaons faed o nd he neraor aped osaons preded by he heory and appeared ha he

deveopen o rbene n a bodary ayer depended on he aon ofrbene n he an srea osde he ayer Then n 194, n eperensby Shbaer & Srasad a he aona Brea of Sandards, nder hedreon of H L Dryden he heory was vered eperena n henrodon o he Engsh edon of Shhngs Bondary Lay ThoryDryden wroe

My w h xma ac buayay w bga ha w. Wh h aaac Schchg a v am wma h am ubac c by h hy. F 0 ya hxma u y fa cm h hy bu u h aha a u fm h c ubulc n h a am ab a hy fh by G Tal Th a wllmmb ay ugu 940 h c wav w h w a a a la a w vy w ubuc. Th hy f aby cb h a fTm a chl chg wa cm quaavly a w a quaavly.

n he heores wodensona srbanes are onsdered n fa, n1933 Sre proved ha he probe of hreedensona dsrbanes of apane parae ow s eqvaen o a probe wh wo-densona dsrbanes a a ower Reynods nber, so he n ra Reynods

nber s gven by a wo-densona anayssfer he eperena veraon of he aaons of Toen andShhng des reaned nsaby n a anar ow even whaped dsrbanes, s no he sae as ranson o a fy rben ow he gap n ndersandng was s aher arge and aeps have onyreeny been ade o frher ndersandng by onsderaons of nedsrbanes, saby of he dsrbed ow, e Frher dob f s yepossbe o sae wh erany how h he appearane of rbene n abondary ayer espeay over a red srae wh a pressre graden, asn ow pas a sphere, for eape s de o nsaby n he bondary-ayerow and how h o he ee of pressed dsrbanes fro rbenen he an srea, or how h hey nera

TURBLENCE

s prevosy saed rbene n bondary ayers was enoned a afary eary sage by Lanheser and by rand ne of he eary rphs ofhe deas of bondary-ayer heory as he epanaon of he rapd drop ofhe drag oeen, for nsane of a sphere, wh nreasng eynodsnbers n he neghborhood of a eran ra nber, whh depends on

everyhng ha an nene he ranson o rbene n he bondaryayer, sh as he degree of rbene n he an srea, roghness of he

Ann

u.Rev.FluidMech.1969.1:129.Downloadedfromwww.annualr

eviews.org




22/29

FLUID MECHANCS-FST HAF OF S CENURY

uac t tod o uppot and otuanc oo o ot attac- nt on t uac. In a tuulnt ounda la cau o t ovigoou ntcang o ontu twn dint tata t taddud can a t wa nto gion o ig pu o paaton o

tat altoug t iction dag i inad t o dag i conidaldcad. T pnonon itl wa t dontatd Eil in aiin 2 o a p and t xplanaton wa givn andtl in 4 wootaind all dag cocint vn at ail low nold nu nducng tuulnc wt a w oo xd on a p an a lattoi w till ing told in ttinn aout gat diagnt in tult xpintall otaind t wit to o Eil and ow tac on t cau gan

T ac o a atiacto tod o ocating ictional itancwt uunt ow gan a. A cpt atatca to o to xpctd and xpint did nt dal wit ig nold nuCoupld wit oula o t ianc cocint i a oula o tditiution o vlocit na a wall In laiu pt owad intpoationoula accoding to wic t itanc cocint vad a t nvo t /4t pow o t nold u and t vlocit a t /7tpow o t ditanc o t wall. ttpt w ad to ow tat toula ad a totical ai ut wn xpint w ad atnold nu aov 0 it wa ound tat t indx / ad to diinid pogivl to /8 / tc.

In 1925 Prandtl pu fowad what bcame kow as his "mx-ghto and alo aud in tat connction tat ontu i a tanalpopt. o ocat na a wall ti wa a valual advanc

anwil ac o atiacto xtapolatin oula o itancand vlocit na a wall continud vigooul and at t Tid ntnational Cong o pplid canc at Stocol Kn wa t tto announc t aou logaitic oula o wall tuulnc otaind t ult o i iilait to. andtl otaind t ulto ipl in a pap pulid otl atwad ( and it latappad tat ot "ational agunt would poduc t a ult

Howv t announcnt n 0 n Stoco Kn wa t tannouncnt o ti aou law wall tuulnc

T lat 0 and al 0 wa a avloul xciting ti oipiical toi o tuulnc.

I n 2 Talo pulid a pap on T tanpot o voticit and attoug uid in tuulnt otion in wic too voticit nt ontu a t tanal popt poning out tat t auption tatontu i a tanal popt involv t auption tat tuctuation in pu in t tuulnt ow do not act t an tanpot

o ontu. Talo voticit-tan toy in act datd ac to ipap on Edd oton n t ato i and to a o t

Annu




only.


23/29

L

das e awaded e sae yea e eqans f e velcy dsn ae n geneal deen n e en-ansfe and e vcyansfe ees , e pnly wen ee s ea ansppedced epeae dsns e. n an append Tayl's 32

pape age & alne eped n eased epeae dsn ne wae f a eaed cylnde and e esls n e vcyansfe eywee c clse e epeena esls an se f e enansfe ey. Teeafe any epeens wee ade n an e assess e elave es f e w ees

Tayl plsed s ded vcyansfe ey n 13and13 and e applcan w n pes n 13 cann e se f yecllecn eleve e neaed an ld anscp f ans papes agan pa f s da e essay) wen swed asewa nsasfacy) pape f ne n e genealed vcy-ansfe ey sayng a e ad pevsly g speclave pls. a e cean a a pape f Tayl's n ane sec saly nsaed ds w densy gades wc was plsed n 13 anscp was aen f sage n y eneay was pa f Taylsdas ze essay and ad een n sage f se cnsdeale e ssssn f plcan avng een ndeed y e ccence f es wld wa

Meanwle eseac was pceedng n len dsn wc ads geness n Tayl's 121 pape n e rodig of h odo Mah

maica Soci n Dsn y cnns veens.Hweve a wlly new decn was gven eseac y e plcan n 13 f Tayl's Sascal y f lence n a sees f papes sng gnaly cnanng ay new nns ang e spcence cves cean a enegy sspan e ecay lence end a gd and celans and enegy speca as Feanss 138) Kn ndced e celan ens dependngn an ncpessle d n ne scala fncn and deved an eqanf canges n a scala wc can e sed an nan ae ae f decay w e asspn a e ean vales f ple pdcsf cpnens f velces a w pns cld e negleced Kn pned a s s ncec e v laens wld ave a peanenendency e seced cpessd alng e as f e vcy andeleved a s cld n e e case. Hweve Tayl swed a wase e negleced eng swn f ean easeens n ne case eee es a e a s n nelec. Tee a endency e velaens e seced n e aveae. T lence s essenally dspesveLae dng e secnd wld wa eaed Tayl a an aygeneal ad s eplaned a e esn wy nfan and spples dd

n always ave a e desnan a e planned e was e cn wa. sppse epled Tayl a spples ae sewn ve ecnysde ecase e lence wa.






24/29

MCHANC R HA O H CNURY 23

K & Howa owed i 1938 a e iecoeaio eoao ivove oe caa ucio o iooic uuece i a icoeieuid, ad caied e dicuio ue wi e yoei a e gao e coeaio ucio eeve ei ae

Wo coiued vigoouy Coiuio cae i o Loiyaii,iiociov, ad Koogoov, woe coiuio oved aicuayvauae Te ae o e diiguied aeaicia Koogoov wa weow o oe diiguied aeaica aiicia, oe o wo adoe o coiuig o e eoy o uuece We ey aw eyica, ae a aeaica, aue o Koogoov coiuioo o e decided a uc eeac wa o o e. Oe woaicuay o eca aayi, ao aeaed. eawie, exeieaad ei-eiica wo o ea uuece wa ao oceedig.

O e woe e exeiea ad eieiica wo ouied.

e oe ie, oweve, e oe udaea eoeica wo evedoe ae oaced exaiaio, o exii ceay e dicuie a oove e. i, oo wa a vauae coiuio.

wa a a eeig o e Bii ociaio i Lodo i 19 a eee a La eaed I a a od a ow, ad we I die adgo o Heave ee ae wo ae o wic oe o eigee.Oe i uau eecodyaic, ad e oe i e uue oio ouid d aou e oe I a eay ae oiiiic I ave uoedo eoy o do o guaaee a e acua wod Bu e ee icoec I ave ead a iia oy ice eeaed wi oe ae aa a oe e a ace a wa coec o wo coe woew i ageed a i wa Heave a e wou go o, ad e wa ig oe oe oiiiic aou uau eecodyaic a uuece.

W G DN H N

Le e eu o oc wave ad ga dyaic Raie ad H ugoioad uied ei ae o oc wave i e ieee ceuy, adE ac ad i aociae ega ei exeiea oevaio aoue ae ie a Hugoio uied (1889. Howeve, ee wa i oe

dou ad couio aou e eoeica exaaio. Te dicoiuiyeeed o vey a Wa e oce o e aociaed w e eoy o aidea ivicid ga, o wee diiaive ocee eeia? e e uicaio o ayeig ad ayo i 19 1 eeed o i e oeig 19 o 191i, e eoeica idea eed o a oudaio ad e way wa oeo ue avace, o o oe ad oe coicaed oe oocwave ieacio ad o e eecio, diacio, ad eacio ooc wave, a i e wo o oace & Seege o exae ad o eucue o oc wave, wi aowace o u vicoiy ad vaiaiowi eeaue o e vicoiy coecie oug e coec vaiaioo e u vicoiy i i uceai Te iveigaio o e ucue ooc wave euied ueica eod. veigaio o oc-wave


views.org

A


only.


25/29

DSE

ucue by he ineic hey gae al llwed lae. In he hal he cenuy he w culminaed in J. vn eumann numeical mehd.

The ealy ae aai may be illuaed by me quain m hepape Rayleigh and Tayl Rayleigh wie unde he heading "e

manen egime unde he inuence diipaive ce "The inveigain be cnideed unde hi head i a vey emaable ne by RanineOn he Themdynamic They Wave Finie Lngiudinal Diubance hil Tan 187 which ecep a limied pa expunded byMaxwell in hi hory o Ha) ha een uch negleced. Thee i hee ane in which Rayleigh ay "I u ae my hae he blame buadd ha Ranine i eeed by amb (Hdodam 16 p. 66In he ex he cninue "Cnduci hea i hee he ime aenin accun and alhugh hee ae ne w eiu deciencie n ay e peenly be niced he memi a a vey denie ad

vance Lae he ee "a lng and ably wien memi by Hugniand ae epeaing ha "Ranine inveigain i epely baed upncnducin hea in he ga ema ha "A wave hi ind i nevepible unde he cndiin laid dwn by Hugni n viciy heacnducin A cle examinain he pce by which [Equain 85]wa bained will hw ha while he law hemdynamic ha beenbeved he ecnd law ha been degaded The eaable hing waha bh Ranine and ugni ended up wih he ame equain.eihe had cnideed viciy

Tayl pined u ha "The pibiliy he ppagain a uace dicninuiy in a ga wa cnideed by e 1848 . He laeae aly ha "I i eviden ha a plane abluely hap ahemaical dicninuiy cann ccu in any eal ga He ee he ineic1heory of gases, and continues "s suggests at eat condction nvciy ae in he cae a eal ga he caue he pducin diipaive hea i will be hwn ha unde ceain cndiin hey ae alucien pduce pemanence ype in he laye aniin.

The udy ga dynamic and high-peed aedynamic pceededeadily and a a mewha inceaing pace duing ay he hid he

cenuy me he m valuable advance wee in he pviin and deign high-peed wind unnel and inumenain Twad he end he12 he nly lecue n ga dynamic I emebe being given in Cambidge England wee a eie eigh lecue by G I Tayl.

In 1 came he Fih Vla Cnge which wa indeed an impaneven he chneide Th cnex had had i eec n highpeedaedynamic and ne he pape a he Cnge wa by Wimpei n"The Biih echnical pepaain he ceide Tphy Cne11 in which he decibed a e aid "he cmbinain which achieved

ucce in he 11 cneide Tphy Cne. weve in addiincieni and enginee wee aleady deaming upenic igh. Amng he

Annu




only.


26/29

UD MHS-RS H O HS URY 2 5

pap a th g th hat a f h w ga ct hghpd w ad a { Ba ad hgh-pd wd ad pta tchq ataac c g Ccc ad ai d acw a hgh

pd ga ad ach Fac VaI th a dcad th ha-c paca a th h

cd wd wa th pac ca ad advac wdg ca apd at hctc Rp dvd pac wha had d a ah w gd a ha wv dhat t I wa a ctg ad ga f ad ah wa wa v

I p v t h h hghgh f what wa d h hafct apat h pv hghpd wd t adqpt b a w d adt-M pagaphca ad ca h athatca th f chaactcaa f c ad f pc w ad hgh appa th adt-a h ad f ad M fd f vt h cg-p h dc at h adta f d f vt c h ad a ad happaac h thd f ccv appa aRagh ad at Hatch-Wdt Ta cca aagwth h ctc d pd a ct a haw ta vaadpth whch cd chagd ccv appat da

a a a h ps a rcoa rsac; ay's cac a vt ad a c fcatg h t f ac th thTaMacc ad t pc w pa a c ca d wh d wa ad a h d-d h ad a f M w-pd w ad t dvp Wadad th ad at Mac C. da ad W R a h dvpf hapg hdgaph hd ad th atat h f a appat qa tat adg t th fa T pfa whch wa v d af dg c ghtth dg ad at h cd wd wa wh th th a tdd C. . L h f aaica ahatica dvp th L a h (a a d Bga) 1947; tac at h a hpc w T ad H a ad h w d dpd dv Ta ad a at wav

I h c a h Va Cg had ad hav p hat th p pvdd h hdgaph hd a pd c ad tha ca p d f vtga h d ca f w wth pa c pat pc

g I ha c h a cdd w a v hgh M ach a wha h cad ta pic pd ad w cad th hp

Annu




only.


27/29

6 LDSIN

soc ge ts coecto t etos cocepto o esstce 9 Buse stue o sock ye o sg tckess ote ou o te suce pessues t te se o te sock ye

1949 Lgt puse ppes o te cto o st o

tecue o eeg ppote soutos to pysc poes uoy . Te tecue te tte ppe s ee te ey use tee s ee cosee scusso o ts coecto t te teoyo igua petutos, ouy-ye teoy te teoy o "e "oute soutos.

Wts ppe in e odig o h oal Soi puse 9 o e eou o supesoc o pst oy o evouto o te s s st tue o y efeee t ey teestg te u scusso o s ojecto c suy s e ge o

usg setopc etos to stuy te ecy o soc ve s peousy ee oe y Fecs te pe cse so s te eeeepote out Wt s goo copy. e guet o te eeees seous ts s te geess o gs 190 ppe o "eeegy stuto e ecyg socks Ws ppe s uyccepte y te oy ocety pse

gts st ppes ee pue 1944 y 948 e s te to ee gee ectue t te eet teto Cogess foppe Meccs Te ectue s o " Metos o pectg peoen te gspee o o gses Lgt spoe te s ppe te

tc o tec pyscst s cocug os e teestgI I w s tt our uersadig o he high-speed ow o gases

s growg rapid; as a mahemacia eieve ha ou edeavos hs ed are mahemaa teues ot o ecse e e ssstg grt ew egeerg adveuesupersoc ighu aso sce we aegeg o grps his proem wh h od ogema he oear paia dferea equao smeg ou hs was a mae fo whch our coeagues te moe udamea pars of phss ma ae e gaeu

XPEEN CE N ECNQUE UEC EO

My poeets epeet ctes tecues took pce te st -cetuy. ee ee tues o spec puposes gspee tues otuuece tues (t c te invesiaion ot o Tyo o te eect o cotcto o tuuece tue ee coecte) s te et o e ee o ou y to gge gge ase ste tues stuets eectc etosespecy o esueets tuuet o ce to cesg useteote eoete te ot-e ecto-ete etos o esugspee tos coetos tuuet o o eteg

eegy spet Th mhods o salzin and phoogaphng id otospouce sctg esuts ete te eto s soke o te

Annu




only.


28/29

2 7

re w an apple ee a ceap cigaree ianiu anniceaclie e el e ceical caing a ace, wre par aw, Sclieren r inereree picue eultricroscope photophs in waer Fage nen

uecal e ave previuly been enine in cnnecin wiabily iveigan, inguace ery an e ucue cwave In e 1 Suwel' elaain e, an e ewaia e were being ue Digial acine cae graualy re anmore ino us. Lae, lagely ne e inpiain vn euann an Peei in e Weiann nue in Irael, eiu ue wa be ae igpee cpuing acnery, bu a wa eally a lae ry, a evennw ee i il a lng way g

Pranl nce l e a e a cnee bulng an analgue acne, b cae e cnclin a wae iel wa e be I i epe

a euann nce a a ee wu be n ue nee epeienigpee cpuain cul ae ver I uppe b were incrrec;we nee b eperien an cpua

ONCUON

Muc a been ie I ave eaaly eie e epain wi abu e aguen cncening ecain, an e elaive ipance aeaic pyc, an engineeing Ang e aer ie are:(a) e begnning agneyynaic, Harann aau 17)on e w ec n nn pc f mc ,Hann Teller n agneyrynac c, e cnnecin wiapyic an e publcain Avn Csmc ctrdynmcs juaer e cle e alcenury; (b) wle cun uc a eerlgical inveigan, ceangrapy, urace wave an ie, ialiipain an arnical appcain Tayl 118 an 1 aneey 1) an allwwae ey, an gepyc al e abiliy raing ae ui an arnica applicain c ineeing anipan eaile uein, wic e ag en icnerable enuia, uc a e e ingularie icuin

of the aerodyn propeties nd design irship shapes an the use byIn uble allw r crwin (1), an railing vice rwieninal aiil in ievaiable in (Binbau, 14; Wage,1 ; Krn Sea 18 ; Sear, 14 an e) ; uneay airlin in ig bnic an in upenic w al e geneal caclain val inea, ce an en i iainal invici in anarier icain een e; () e cnnecin ui ynaic an ea ane; ( raree gae an elaain eecI lleebe vviy Arur anwi r enain wi aLangley e uc ing a urbulence in un pipe, an e epeiin eynl epeen by Bane e, Ean, an Tayl

Ann

u.Rev.FluidMech.1969.1:129.Downloadedfromwww.annualr

eviews.org




29/29

2 DEIN

an al iin te pible wae bein a pee epning ta texee ben a ylne w me ng a nt tenig in eey nigb in Aaen a te t ime te Aaen Cneene n2 an nally lng e pblem wt allally ne epia

) jet an aiie an () m eleSme qatn ae been nle n atle. eap tee ae

reaer w tik te tile l ve been mpe ter we rqtatin an le te matte am emne a bie eiew in Nu a b n eatin. Te we eiew wa Hal t b qtatn te te al l ae been.

Annu




only.

Annual Review of Fluid Dynamics Vol 1, Goldstein S.

Documents

Transcript of Annual Review of Fluid Dynamics Vol 1, Goldstein S.