Boundary Lyer Theory

754 XXJV. Frce turhnlent flows; jets and wakes Rcfcrenccs 755
Exp. I1
1.36
0 2.34
0 3.65
A 1.19
A 2-01
Fig. 24.12. The mixing of coaxial turbulent jets
of different velocities and temperatures in a pipe,
after S. R. Ahmcd [la]. Variations of the velocity
along the nxis of the pipe n) for vnrious velocity
rntios U* = urro/~so at a constant value of the
temperature rntio O*; b) for vnrioua values of t.lie
temperature ratio Q* = Olro/Oso at a constant
value of the velocity. F* = frro/fso denotes the
area ratio of the inner jet Lo the whole jet
two cases: 1, two-dimensional [low above a lincar source of heat placed on a horizont,nl
floor and 2. &xi-symmetrical flow above a point-source. In both cases the width of
the velocity and temperatmure profilc increases in clircct proportion to the height
abovc the floor, x. In the two-dimensional cnsc thc vcloait-y rcmains constant at dl
heighbs, whereas the temperalure dccreeses as x-1. In thc axially symn~etrical casc
the velocity is proportional to 2-113, the temperature being proportional to x-514.
The two-dimensional case was treated theoretically on the basis of Prantltl's mixing-
length theory (tmnsport of rnomcntum) as well as on thc basis of G. I. Taylor's
vorticity tmnsport tlteory. The nxially ~ymmctricnl casc could bc invcst~igntcd only
with the aid of Prandtl's thory bccausc G. I. Taylor's tlicory brcnlts clown in thig
case. Measurements performed for thc axi-syn~met~rical enso conf rm t.11~ thcorrl~ical
cslculations. The diffusion of temperature behind a point-source and behind n Linear
source placed in the boundary layer on a flat plat,c were investigated experi~ucntslly
by I