The Reduction of Skin Friction Drag 



600 8001000 



2000 



4000 6000 



y + = 



yu 



Fig. 5 - Velocity profile in the wall layer in flow of 

 flocculated thoria, from Eissenberg and Bogue (1963). 

 Nondimensionalization by shear velocity with small 

 empirical correction c. Solid line is Newtonian pro- 

 file. 



Another method of changing R , suggested by G. F. Wislicenus (private com- 

 munication) is to change the boundary condition, by making the surface flexible. 

 Again, the action of such a surface depends in a detailed way on changing the 

 phase relationships, and thus the Reynolds stress. To make this distinct from 

 the violation of the law of the wall mentioned above, we must have the wave 

 speed in the wall well above the free -stream speed. A detailed analysis based 

 on energy considerations (Lumley and McMahon (1964)) shows that the situation 

 is rather complicated, due to the fact that, although over a rigid wall no small 

 disturbance can extract energy from a linear profile fast enough to maintain it- 

 self, while some large ones can, this is no longer true over certain flexible 

 walls. Thus, while the wall changes the energy budget of large disturbances, it 

 also provides a mechanism* by which small disturbances can extract energy. In 

 Fig. 6 are shown the phase relationships calculated for small disturbances. It 

 can be seen that, for this wall material, there is always a wave whose speed is 

 such that it can extract energy. Evidently only a wall which is prevented from 

 moving laterally is worth examining. 



Conclusions 



This outline has surely not exhausted the possibilities of changing (or elim- 

 inating) momentum transport in a turbulent boundary layer. For example, we 

 have not discussed the possibility of influencing transition by oscillations of the 



'^Similar to Rayleighwave propagation in the wall — the class B waves of Benjamin 

 (1963). 



927 



