Lumley 



SPRINGY 



I 



LOSSY 



il 



DOWNSTREAM 



MASSY SAINY 



BOUNDARY CONDITIONS FOR SEMI - INFINITE 

 LINEAR VISCO-ELASTIC SOLID .lossy 



i 



DOWNSTREAM 



il u 



IGAINY 



SPRINGY 

 LOSSY I 6AINY 



PHASE RELATIONS 

 IN VISCOUS REGION 

 OVER RIGID SURFACE 



PHASE RELATIONS IN 



VISCOUS REGION OVER 



FLEXIBLE WALL 



SPRINGY GOOD 



MASSY BAD 



LATERAL RESPONSE BAD 



Fig. 3 - Small disturbance phase relations in the 

 laminar boundary layer between the critical layer 

 and the inner viscous layer: first order modifica- 

 tion by flexible wall. 



Non-Newtonian Additive 



The second method not dependent on a change of profile (Giles 1964) depends 

 on the use of a non-Newtonian additive of viscoelastic character. One may ex- 

 pect that if the apparent viscosity to a temporally sinusoidal simple shear in- 

 creases with frequency, then the flow would be more stable to progressive waves, 

 since the history of a material point involved in such a wave is unsteady. The 

 opposite case is of greater interest for real fluids, and a recent analysis (Wen 

 (1963)) indicates a destabilizing effect, but that may be because a model was 

 used that is not materially objective. 



Drawbacks of the Conventional Techniques 



Most of these techniques are, or have been, under experimental investigation 

 by various groups and individuals and show some prospects of success, but in 



920 



