Wave velocity in parallel flows of a viscous fluid

1973 ◽  
Vol 58 (4) ◽  
pp. 703-708 ◽  
Author(s):  
Chia-Shun Yih
Keyword(s):  
Viscous Fluid ◽  
Wave Velocity ◽  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Parallel Flows

It is shown in this note that the velocity of unstable or neutral waves in plane Poiseuille flow or plane Couette-Poiseuille flow, or of axisymmetric waves in Poiseuille flow, stable or unstable, must lie within the range of the velocity of the flow.

On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow

1960 ◽  
Vol 9 (3) ◽  
pp. 371-389 ◽  
Author(s):  
J. Watson
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Complete Solution ◽  
Equations Of Motion ◽  
Plane Poiseuille Flow ◽  
Wave Disturbances ◽  
Parallel Flows ◽  
Infinitesimal Disturbance ◽  
Non Linear Mechanics ◽  
Finite Disturbance

In Part 1 by Stuart (1960), a study was made of the growth of an unstable infinitesimal disturbance, or the decay of a finite disturbance through a stable infinitesimal disturbance to zero, in plane Poiseuille flow, and that paper gave the most important terms in a solution of the equations of motion. The greater part of the present paper is concerned with a re-formulation of this problem which readily yields the complete solution. By the same method a solution for Couette flow is obtained. This solution is only a formal one for the present because the conditions imposed in deriving the solution may not be valid for Couette flow; this flow is believed to be stable to infinitesimal disturbances of the type considered.

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