Fink and Naudascher 
solutions are twofold. First, there is the closure problem in the 
equations of motion, if the flow is turbulent. And second, even if one 
of the widespread effective-viscosity assumptions has been introduc- 
ed to describe the structure of turbulence, there is the difficulty in 
handling the partial differential equations. 
In the following, we shall deal solely with methods designed 
to overcome the latter difficulty. There are several well-established 
methods to solve the parabolic partial differential equations of the 
boundary-layer type. In the last decade, some powerful methods for 
numerical treatment of the governing equations were put forward 
(e.g., see Ref. [1]). Further, the application of the generalized 
Galerkin-Ritz Method (i.e., the G-K-D method) has proven to be very 
useful eal , although this method has not yet reached perfection. 
In this paper, we shalluse the well-known integral method 
combined with suitable similarity transformations as initially propos- 
ed by von Karman. The advantage of this method lies in the relatively 
simple, closed-form deduction of approximate solutions, which in 
most cases are good enough for engineering purposes. Moreover, the 
method is very helpful when applying numerical procedures to flow 
situations complicated by special boundary conditions or by density 
stratification etc., because it allows to predetermine special features 
of the solutions like e.g., the behavior in the asymptotic ranges. 
A disadvantage of integral methods, if used in combination with 
the conventional similarity assumptions and the corresponding sim- 
plifications, is the fact that they can rarely be extended to flow confi- 
gurations which differ from those for which the assumptions and sim- 
plifications were designed. This may partly explain why not much 
progress has been achieved in this field since the classical works of 
Tollmien (1931, small deficit wake [3] ) and Schlichting (1933, free 
jet in stagnant surrounding [4] ). 
There exists a close relationship between the flows treated by 
Tollmien and Schlichting and the laminar free jet in a uniform stream 
to be treated in this paper : in that part of the field where the velocity 
in the jet is an order of magnitude larger than the free stream velo- 
city, the flow can be treated approximately like a free jet in other- 
wise quiescent fluid. On the other hand, at some distance downstream 
from the flow origin, the excess velocity along the center-line becomes 
small in comparison with the velocity of the external flow, irrespec- 
tive of the initial strength of the jet, because the excess-momentum 
flux is distributed over an ever-increasing diffusion zone ; in this re- 
gion the same approximations as in wake flows should hold true. 
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