Panel Discussion 



e./ii_liI2 « 1 



The latter assumption permits one to construct the solution in the form of a 

 power series of the small parameter e . 



In all cases the coefficients of the expansions are defined by systems of 

 partial differential equations. These systems of equations were solved numeri- 

 cally by application of implicit difference schemes. 



From the analysis of the behavior of the solutions obtained in this manner, 

 some qualitative conclusions were reached in regard to the properties of the 

 flows studied. For example, with increase of the parameter i, = wx/uq the in- 

 fluence zone of outer disturbances is displaced closer to the edge of the boundary 

 layer in the first case, but closer to the place surface in the second case. 



In the case of the random disturbances, the free- stream velocity fluctua- 

 tions permeate the boundary layer most of all at the relatively large values of 

 the scale of turbulence. In this case the velocity fluctuations within the boundary 

 layer may exceed those which occur outside. 



DISCUSSION 



K. Wieghardt (Universitat Hamburg, Germany) asked whether the term 

 B^u/Sx^, which is neglected in the derivation of the boundary -layer equations, re- 

 mains small in the presence of the assumed disturbances, as could easily be 

 verified by examining the resulting solutions. It was stated, in reply, that the 

 derived coefficients were examined for their variation with frequency and down- 

 stream distance x , but it would be necessary to examine the paper in detail to 

 determine when B^^/Bx^ became large. 



Some Problems in the Numerical Solution of 

 Three-Dimensional, Incompressible Fluid Flows 



S. A. Piacsek 



University of Notre Dame, Indiana 



Current attempts at numerical calculations of three-dimensional, incom- 

 pressible flows on digital computers may be divided into two categories: 



1. Velocity -Pressure Approach: In this method one uses the time- 

 dependent Navier- Stokes equations to find the velocity components from a time 

 iteration, and the pressure is found from a Poisson equation that one obtains by 



1615 



