Boundary Lyer Theory

630
XVII. Origin ot t.~~rhr~lrncc J l
This ineqnnlity contnins Rayleigh's criterion from eqn. (17.19) as a special case
ant1 rcs~~lt.s wherl 7o = 0 is ns~nmcd here; we then find that 1 + 5 > 0. The stability
calcnlntion which led to eqn. (17.23) took into account disturbances which were
not ~icccssnrily axially symmetric; the 1n.th.x turned out, to be the "moat dangerous"
oms ant1 detcrminctl (he litnit of st.:~l)ilil.y implied by thc ineqrlnlity (17.23). l'ignro
17.36 shows an example of an unstable flow which contains vortices in the shape
of spirals. If. Ludwirg's tllcory has bccn compared withexpcrirnent.al resulk [134]
in Fig. 17.36. Every bnse flow invcstigated experimentally is represented by a point
in t,Ilc I;, 271 plane. The opcn ant1 full circles characterize stable and unstable flow,
respectivciy, it being riotcd that vortkcs were observed for the latter. It is seen
t.hn.t, IT. I,utlwicg's st.:~l)ilil.y crit,crion from rqn. (17.23) is fully confirmed hy cx-
Fig. 17.37. R.nngen of Inwinnr nnd l,rrrl)~tlet~t, flow in n~~tii~luu I~C~IYC~II two concctltric. cyli11tlc.r~;
innrr cylinricr rotntrs. outm cylitldrr nt. rn~I, in prmRltro of nxi:d flow: plot. in t.crr~lu of 'l'r~~lor IIII~II.
I,t.rT,, 1111rl IIIIIIII#('). R.,; tlll~ll~11~l~llll'l1(H 1))' #I. I