ON THE VALIDITY OF A GENERAL SIMILARITY 
HYPOTHESIS FOR JET AND WAKE FLOWS* 
Leo Fink and Eduard Naudascher 
Untverstty of Karlsruhe 
Karlsruhe, Germany 
ABSTRACT 
The validity of a new analytical approach by which 
the development of any free-turbulence shear flow 
in an incompressible fluid is predicted through the 
use of a general similarity hypothesis, has been 
tested by applying it to laminar jets in uniform un- 
confined streams. Because of the lack of experi- 
mental data, the analytical solutions derived for 
plane and axisymmetric jets in coaxial parallel flow 
were comparedtocorresponding solutions based on 
coordinate-type perturbation expansions. The sa- 
tisfactory agreement obtained in allcases suggests 
strongly that the new similarity analysis is a valid 
approach which, if used with suitable turbulence 
hypotheses, will also predict successfully the cha- 
racteristics of any turbulent jet and wake flows. 
INTRODUCTION 
Jets and wakes are the most common examples of free shear 
flows. Since the foundation of the boundary-layer theory by Prandtl 
in 1904, they have been the subject of numerous investigations both 
analytical and experimental. Nevertheless, reliable solutions are 
restricted so far to simple cases like free jets in stagnant fluids or 
small-deficit wakes. On the other hand, it is just the more complex 
flows like jets in external streams which are of special interest with 
respect to applications in fields ranging from Aerodynamics to Civil 
and Chemical Engineering. The reasons why there are no common 
* ) This work is part of a project sponsored by the Sonderforschungsbereich 80 «Ausbreitungs- und 
Transportvorgange in Stromungen» at the University of Karlsruhe, Federal Republic of Germany. 
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