General Stmtlartty Hypothests for Jet and Wake Flows 
1/2 
Se (SY Ge a(S) 
0 for j = 0 and y 9, for j = 1 
1/2 
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8, 8, 8, 8, 
This twofold asymptotic behavior suggests the conclusion that the 
presented solutions render also reliable predictions in the transition 
region, In any case they are superior to the conventional similarity 
solutions, which display correct behavior only at one limit. 
Unfortunately, there are no data available to check the va- 
lidity of the derived solutions by experiments. However, a compa- 
rison is possible with the analytical investigation of laminar coaxial 
jet flows by Wygnanski [10, 11] . Wygnanski starts with the same 
governing equations (Eqs. 1 and 2). But instead of a similarity as- 
sumption, he uses a coordinate-type perturbation expansion for the 
plane- and axisymmetric jets in still surroundings (Figures 6 and 7). 
A comparison of Figures 2 and 6 reveals that the two solutions can 
be made identical by mere translation. This fact allows one to es- 
tablish a correlation between the definitions of streamwise coordi- 
nates used in this paper and by Wygnanski. The difference for in- 
termediate distances x between the solutions in Figures 4 and 7 
arise mainly because of the fact that the integrals I,,1,,1, are 
not constants but take different values at the two asymptotes ''free 
jet in stagnant fluid'' and ''small-deficit wake". 
CONCLUSIONS 
Approximate solutions have been derived for the decay of the 
maximum axial excess velocity and the growth of the characteristic 
length scale of laminar plane- and axisymmetric jets in uniform 
infinite streams. In contrast to the conventional notion that there 
exist no similarity solutions for free shear flows with more com- 
plicated boundary conditions, the laminar coaxial jet was successful- 
ly treated by a new similarity assumption, for which the conventional 
velocity-type representation of the flow-field is replaced by a mo- 
mentum -type description. The solutions derived with the aid of the 
momentum and energy equations, both simplified by the boundary- 
layer approximations, were found to apply over practically the whole 
range of axial distances, excluding only the immediate proximity of 
the flow origin. 
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