Fink and Naudascher 
I I i Eee 
Wz ie ae eee bey he ee 0 
= + — = - 
fn( 4 uF? (Sig 2 oe ) I H S) 3) 
2 0 
and 
i I, L v Dr - XG 
Fe Stier see sere ee 
u 2 H 1 
for plane flow (j = 0) and axisymmetric flow (j = 1), respectively. 
The constant of integration was obtained from the boundary condi- 
tion x/0; —_ x 9/0; ; U, /U*» 0, which defines the virtual kine- 
matic origin. The value of x9/ 6; must be determined from expe- 
riments. 
Now the growth of the length scale RX (x) can be determined 
from the momentum equation (Eq. 9) and Eqs.14 and 15 after eli- 
mination of the parameter V = Us /U*. 
All analytical solutions are presented graphically in Figures 
2 to 7. They show the following general characteristics: 
a) For small distances from the flow origin, one obtains the verified 
asymptotic laws for the free jet in otherwise stagnant fluid, that is 
1/3 
Us d x U A ae) al 
wae = ton 1 Se (@? 
for. j* =80 ‘and for] =1 
S ae f he 
ea Va pedis 
0 0 1 1 
b) Far downstream, the solutions converge toward the well-known 
power laws of the respective wake flows, that is 
IZ92 
