Boundary Lyer Theory

514
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XVII. Origin of turbulence 11
e. Effeotu due: to hcnt trnnofer nrld compreusihilityt
1. ln~rotlurtor~ rctmnrk. 'I'll(: t.ltrorc:t,icnl nntl ~xprritn(:nt,nl rns~llt,s coticcrtri~~g
tr:l.tlsil.ion closcril)ctl itt tho prcv-(:(ling sc:c:t,ions are valitl only for flows at modcmtc
sl~:ctls (itic~otlrI)rc~ssil~ln Ilow). 'l'lln rll'cc:l. of t,hn compressibilit,y of thc? firlit1 on tmnsit.iori
h:~s rcrntll,ly Iwcn rxl~n~tsl,ivcly invnstignt,ed urltlcr the ~t~itiid~s from nerort:~.t~lic*nl
c:t~ginrc:ring. In t.he c::l.so of'cornprrssil)lc Ilows, apart, from tho Rlnc:h nrt~nl)rr,
it, is t~crrcss:~ry t,o hltr it1t.o :~cc:onnt, ono ntltliteional, itr~port~nnt pnr~~nct~rr which is
ro~~~~c,rt.rtl \vil.l~ t,l~o ~:rt,c, of Ilrnt, t.rnt~sl'c:rrctl Ixtwccn t,llc: ll~~itl ant1 the wall. \Yhcn
I,II(% I111itl is i~~(~o~~~~~t.(*ssil~l(:,
lt(~~t, WII IN: vxd~;t,t~gwI l~~:t,\v~:rn Ih: w:i~ll :I.II(I I,IIc ll~ti(l
i( 1 11(, (,(~t~~~)t~~~:~t,~~~~:
of t,l~(: \v:~lI is I~igltcr or lowrr t,h:~~ th:~t, of t,he fIui(1 hvitlg
IKISI. it.. 111 1.11~ c:n.sc: of' :L (:otn~w(~ssil)lc Il~~itl, 1.l1c h(~iI, cvoIvc(1 in 1.l1r I)ont~(l:~.ry l:iy(\r
I~ro(l~~c~t*s :III :i.tltlit,ion:bl, itnl)orl,:~trI, inflnonce, ns nlrontly sltown in (:II:L~. X I1 1. 111
rit l1c.r (.:IS(: :I t~Itcrtnnl l~ont~,li~ry I:~yrr (I~:voIoI)s in a(l(lil,iotr 1,o tho vc:Io(:it,y I)oun(l:try
1a.y~-r ant1 plnys it,^ pnrt in the dctcrmin:~t,ion of tho inst.nl)ilit.y of n smnll dist,urbnnoe.
r 1
Lhr t~l~rorct.i~aI ar~tl cxpcrirnc~ntd rotisitlcrnt~iot~s which wr are abor~t t.o discuss will
show t.11nt. for t.he s~~I)sonic flow of n ~:LR, lwnt. trnnsfer from t,lle 1mtntln.ry Inyer to
t,hr wnll exrrt-q n st.n.l~ilizing influcnc-c, wltilr Irrat transf'rr from t,he wnll to t .1~ pas
11ns the opposit.c cfT(~:t,. I3ot.h of t.hcsc nrr reversed for the fiow of a liquid. For srlprrsonic
flow. n new t,ype of unstable rlist,urbnnco is possil)lr ~ hich responds to t,he tmnsfrr
of 11ca.t. in nn entirely tliffcrcnt mnt1nc.r.
2. Tlw effcct of lmnt frnnsfor in iucompressible flow. Sornr of the main frat,urrs
of t,l~c rlkct of f.ltc t,r:~tlsfi~r of 11c:n.t from t,lx w:dl t.o t,lw fluid on t.he st.aldit,y of n
Inn1inn.r I~ot~tttln.ry 11iytv. rrtn ltr ~v:tdily r(w)gnizrd rven in the rrrsc: whrn tho flow is
incotn))rtwil,Ic. Wc shrill. t,llcrcli)rr, cxl~lai~~ it. first. in t,llis simplifird form. The first
exprrirnrntnl invrst~ig:it.iotts on t.he inflltener of 11rn.t t,ransfer on t.ransit.ion were perli)rrnrd
some t.imc ago by W. ],inkc [ 13 I 1. \\'. I,inltc measured t,hr c1ra.g of n vcrt,icnl
hrakd ~)la.tc plncrtl in a horizontal strrntn in a rnngc of length Rcyllokki nlllllbrr
R = 105 to 106, nntl ol)srrvrd t.li:rt. Ilc~nling rar~sc:rl it. to inorrase by n Inrgc ntnor~nt,.
11e conol~ttlcxl ftwm t,llis incrca.sc, qnilr rotwrt.ly. t,llnt, t.hr l~cat~ing of the phtc cnrlficd
t,he t,rnnsit.ion Itrynoltls numl~cr t,o dvrrrase.
Now. if t.lw wall is Ilot.trr than Ihc. llllitl ill thr frcn strmni, we Irnve TI,, > T, ant1
tIw t.t-mpcr:it~~t.c* gt.n.tlirnt. n.t Iltc. wnll is nc*)mti\.c: (t17'/tly)w < 0. Since for a gas the
vis(.osily ittc.r(~asc-s wit11 tc~t)i~)t~~~:~t~~t~(~ :iwotding to ccln. (l3.3), we mnst. have (d/l/dy)fi;
< 0. Since t h vclocit,y grndient is positive nt t,Ilc wnll it follows from ~clll. (17.15)
tlmt.
A nnmcrirnl cnlcul:tt.ion l)y '1'. Crl)rc:i nntl A.M.O. Smith [221 fi)r air cwnfirmrtl
the (l(:crcnsc in t,Ile crit.icn1 IZ~~ynt~I~ls IIIIIII~N:~ for I,ltc ons~t, of i~~sl~al)ilil,y
flnt plntr, nntl n sinlilnr tlrcrrnsc in t,ltc: I.ru.nsilion I (;On(:, tllc tlinit~nsion:~l
irlc:rrnsos in invcrsc. proport.iot~ 1.0 dl. 'I'll(* rcsrtlls for :I. coolctl \vr~lI sl~ow tilt!
cxpcctcd tlc-sl.nbilizing cll'cct for liquids. In t.hc t.ltc:o~.y of' A. It. Wrizz:l.n, t . 1 only ~ inflr~encc
of hmt, transfer, other thn on t,ho rncnn vrlooil,y j)r.olile, is t~11rougll t.Ilr krnperaturn
rlcpenclence of the viscosity. A more oornplrt.e (11c:or.y by It. I,. 1,owell and
wntor boundary laycr on :L flnt platc, .aflcr
A. It. Wwmnn, 'l'. Okilr~~r~rn atlrl A. M. 0.
Smil.l~ [2RO)