Boundary Lyer Theory

352
X'I I I. I,:ur~i~~ar Imt~t~clary hyrrs in corr~p~r~riil~lr flow
l h vn111c.s of/,,," lor tlifTornnt vn.lrlcs of A', are seen plol,tcd in t,crms of P in Fig. 13.15.
It is rcvognizrtl t,llot n chnngo ill pmssrrrn grntlicnt cxcrt,s n n~uch sbronger it~flucncc
on I,,,", nntl 11c:llc:c: on the sho:~ring stxoss n.t the w:~.ll, when t,l~e wall is I~cntocl (Xu, >0)
1,11:111 WII~II t l ~c I:~l,l,c,r is aoolrtl (A', ( 0). In t,I~e mngo of ncgat,ive vnluos of P there
vxisl, l,\vo v:~l~ir.s of r,,, fnr (YI(:II v:l.ltlo of /I. 'l'his is n consoqllonoo of t.ho rxistcnco of
Lwo soI~~l,iot~s in l,l~is r;tngc, ns n~r~~l,ion(xI wrlivr. WIICII l,l~o w:tll is n,(li:~l)n,l,io (AS,,, ==O),
I,II(: low(-r I )~;IIIC~I of' t,l~(: CII~VC yi(,ltls 11cp1,ivc V:I~II(~S of sltcnring s1,rcss wl~id~ j)oinLs
t,o rtwcrsc Ilow. When t,hc wall is hcnt,cd (A',, > 0) il, is possible to find sufficient,ly small
valrtc~s of p -- P,,,,,, for w11ic:h I)ot,l~ vxlncs of I," arc ncgnt,ivc, that is for wl~ioh the
flow 11:~ rcvorsc~tl it,s dirccLion. 1 n the c:~so of :I coolctl wall (8, < O), 11oIh valrles of
I,," ran Im positive, 1.11al. is 1)0(,11 can r~prcscnt~ non-separated flow patrlmns. It is
swn, fin:~.lly, Ifhat, snp:~m.t.ior~ (I,,," =O) rnovcs in the tlirect,ion of smnllcr pressure
risw :IS t11c l.cmprr:~.l,~~rn of 1,Iw wall is incrrn.sctl.
III ortlvr t,o t,r:~nsform fro111 1,11o vn.ri:~l)lc 11 f,o the pl~ydoal t1isLnnc:c y, it is ncccssnry
1.0 111 ili.xv vqns. (I :1.H), (1 3. IO), (1:1.24), (I R.25) nntl (13.62). It is then found tht
Y'ho f:rct,or nl~oatl of t,hc ir~togml is comrrrlt,cd from cqn. (13.53), and the func1,ionnl
rcl:tI.ion b(:t,woon z nntl 2 IIIIIS~, bc tdic11 from cqn. (13.5G). According to eqns. (13.46)
:LII(~ (l3,(;2), I,IIc int,~gr:bncl is
I