Numerical Computation of the Stability of Plane Poiseuille Flow

[+] Author and Article Information
L. Wolf

Artificial Organs Division, Travenol Laboratories, Inc., Round Lake, Ill.

Z. Lavan

Department of Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.

H. J. Nielsen

Sargent and Lundy Engineers, Chicago, Ill.

J. Appl. Mech 45(1), 13-18 (Mar 01, 1978) (6 pages) doi:10.1115/1.3424216 History: Received December 01, 1976; Revised June 01, 1977; Online July 12, 2010


The hydrodynamic stability of plane Poiseuille flow to infinitesimal and finite amplitude disturbances is investigated using a direct numerical technique. The governing equations are cast in terms of vorticity and stream function using second-order central differences in space. The vorticity equation is used to advance the vorticity values in time and successive over-relaxation is used to solve the stream function equation. Two programs were prepared, one for the linearized and the other for the complete disturbance equations. Results obtained by solving the linearized equations agree well with existing solutions for small disturbances. The nonlinear calculations reveal that the behavior of a disturbance depends on the amplitude and on the wave number. The behavior at wave numbers below and above the linear critical wave number is drastically different.

Copyright © 1978 by ASME
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