Boundary Lyer Theory

482 XVT. Origin of tmbulcncc I c. Effort of oscillnhg frrc? st,rcn~n on t.rnnnit,ion 483
process of transition from ltbmin~r to turbulent flow is the conseq~~cnce of an inshbility
in t.1~ laminar flow, enilnciatcd by 0. Reynolds, is hereby completely vindicated.
It. certsinly represents a posaiblr: and observahlr: mechanism of transition. The question
as to whet.11~~ it pints a complet,e picture of the process and whethcr it constit~ltes
the onhy nloahanism oneountcrcd in naturo is still at prtxent an open one. The latter
cjt~:st.iotis now oconpy t.hc at.tcnt.ion of many research workcr*.
e. Effect of oscillnting free stream on transition
Aftrr it hntl bccn dincoverccl with 1.11~ aid of the oxprin~cnt drmrihed earlier thnt. the intensit.y
of turbulenc:c of tho cxternnl stream, thnt. is thnt the preaence of an irreguhr tittle-dependent
flnrtnntion in t,he free strcnm, cxert.ed a strong inflnence on transition, it was natural to nndertnke
st,ndicu on t,ho chct of regular fluctnnt.ion in the free stream on tratlsi6ion. The effect of a
nnperin~ponrd flnct,unt.ion of smnll nmplit,udc (E < 1) in an cxternnl stream U(z, 1) of the form
on tho ~trtwt,urc of n lntninnr bonndnry lnyer w~ diucnwed in SBCB. XV n 3 nnd XV e 3.
Sincc the Il*ynolils rlnrnbrr nt. trnnnition clrrrmnr*r ronnidorsl~l~ RR tho in tan nit^ of turbnlcnrc
inrrrnru, it iu plnllniblc Lo suppoue Lhnt n ainlilnr erect nhould occur a8 the amplitude d u =
~111 of the periodic cxternnl stream is 111;de to increw. The effect of an oscillation euperimposed
on the external strcntn on thc transition of a hminnr boundary layer was clarified experimentally
by J.H. Obren~ski nntl A.A. Fejer [63a] arr well aa by J.A. Miller and A.A. Fejer [60a]. Them
inveetigntionu conwntrated attention, in the first place, on the boundary layer on a flat plate
(Bl~ius profile). In this cnse, the velocity clintribution in the externnl stream is
Hcrc {J, is the tin~c-avcrngc of thc frco-strcnm velocity which is independent of z, dU is the
nn~plitudc of the temporal Rnctuntion in the external stream, and n denotea ita circular frequency.
'rho mcnsurcn~enb rcported in 163~1 werc performed in an incompressible stream with
and with frequencies of n = 4 Lo 62 sec-1.
Them very carcful experin~entnl invent.iptions yielded the following emntial reaults:
(a) The c-riticnl Rrynolds nnmbcr of tho start of transition, R,,fr = Urn zw/v dcpends only on the
arnplitudc AU/Um of the external fluctuation.
(h) Thc dimcnsionlr.s trnnuition length, thnt in the distance between the start of trnnuition and
itn ronil,lrtion, R,,f - RZsc, depcntls only on the frequency of the externnl oscillationt.
(c) '1.11~ record showing the varintion of velocity with time demonutratm that the line of transition
is chnrart~rized by n regular and intermittent transition. The meaaurementa led to the conclusion
thnt trnnnition rnn hc t~rscribrcl by the following "non-steady" hynoldu numbw:
Sinrc thr rhnrnrlrrirtic length of tho cxtrrnal, oscillnt.ing stzrnm iu C - llm/n, it, iu po~sible to
cxprrw the ~~non.~tt~ntly" I~tyold~ nnmbcr in thc form
uz (A u/rrm)
RNC =
2nvn r'
llrre All/l?, in the rlitnenuionlr~~ nn~plitude of tile impredsed oscillntion and ns/lJ: is itR dimensionlr~u
frrqrrt-~~t*y. 'I'hr n~mnnrrn~rnb showd tlint the llcynolds number Rz.t, = 11, ~tr/v nt
- --
t Start of t.rnnnition nt R,,(, .- (1, .rl,/v -- lower curve in Fig. 16.10. Complct,ion of t,ranuition
nt. R,,I, - 11, .rl./l* - nppcr ctrrvc it1 Fig. I ti. 16. Over the t1iut.nncc from zt, to xr it is observed
thnt Ihr intr:r~~~ittr:r~cy fndor incrcnucu fro111 p = 0 to y = 1; this is interprctcd by t,hc statenwnt
thnt in t.liin zone we ohnerve "trannitional t~~rbulcnce".
the point of t8rnnuit~ion warr always con~itlcrnbly reduced con~pnrctl wit,l~ that for nhtionnry llow
when t,hc %on-st.eatlyV Reynolds number am Inrge, i. c. whcn RNS > 27000. In t.l~c.sc: rxpcriincnt.s.
t.rn.nnit.ion on tho flnt p1nt.c in ut.nlionnry Ilow s(.nrl.ctl nt. R,,,, -- 1.8 x 10". At.t.or,li~lg to
Fig. I(i.l(i. thin vnluo of Rz.1, cor~.cnp~ntI~. np~)rt~~in~nLoly. t.o n tnrl~rtlet~co itrlr11nit.y of T 0.230/,,
in the cxtnrnnl nt.rennt.
So far, n nnt,isfnctory theory of ut,nbilit,y for houndnry lnyors in t,hc prcocnco of nn oxt.crrinl
o~cillnting utrcntu doen not cxiut {I I a]. 011servnt.ion of intern~ittnnt t,nrl~ulcncc i r ~ t.11(! I~rrwt%tlrr of
n frro-st,rcntn oncillntion ~IIOWR thtl its freqrroncy fl, is of thc antnc ortlor of n~np~it.~~clo nn thnt, of
nntnrnl. neutrnl disturbnncer of the Tollrnie~l-Scl~licl~ti~~g typo fro111 ntnhilit.y t,l~eor.y; sm also
I'ig. Ifl.18. The freqnenry, ,I, of 1.l~ oscillnt~ing flow invcst.igntml Irwc \vnn ~ninllrr 11y 11 I':u:tor of
ahont 100 t.hnn thnt in t.hc nnl.urnl, nc~rtrnl tlint.nrbnnccs.
A review of Ilte prorcns of trnnsition in thr prcnrnrc of frrc-strrnnl o~rillilt~io~ln uils rrrrntly
prrhlinhrd hy ILJ. l,ochrkc, M.V. Morkovin, nntl A.A. Fcjcr 14HhJ
(G) Conlcscencc. of 1.11rLulcnt spot.s ink) :I fr11l.y t1cvc~lopc:tl t.~~rl)~tlt*~rt. I)OIIII~~:LI.~ 1:13't~.
In most CRRCR, t,hc t,rnnsit.ion frotn t,r~t.l)ulc:nt spvt,s (.o I.ully tlevclopotl (,III~IIII~W~I~ is
associated with the furrnntion of a separat.ion bubblr, ns nlrwtly ~nont.ionctl in c:otlncxion
wit,ll Fig. 10.10. At, tho present, time, only stngcs (1 ), (2) ant1 (3) nrr :~mrnnt)le t.o :L
t,hcoretical analysis. The complete clnrification of the ~~~nnining stngrbn will rrq11i1.e
rn~lch ntltlit,i~)nnl t.l~corc~t~icid resenrcl~ work.
(1) Stnbtr now
(2) I~'11~1nI~lr '~f~ll~~~l~~~~-H~~l~li~~l~li~~u
WIWR 01--x I?,,,,
Q 099 9 9
lominor I- Ironsilion
A,,,,
R c
JdTig. 16.23. Itlcnlizcd sltclrh of t.rnnsil.ion zone ill lhr I)O~III~~ILT~ 1:1~t:r 011 11 Ililt l~llltP 111 Z~.I.O i11t.i.
clcncc after P. M. While 11073