Solution of a nonlinear stability problem connected with the motion of a fluid between two parallel plates
Abstract
The initial value problem is studied numerically for the case of an infinitesimal disturbance imposed on a fully developed plane Poiseuille flow in an incompressible viscous fluid in steady motion at a Reynolds number R slightly greater than the critical value R sub C above which small velocity perturbations or vorticity waves may be amplified. If their amplitude becomes too large a nonlinear theory is required in order to follow their evolution. The solution of this problem is studied by applying an extension of the finite element method to operators of parabolic type both in the cases of a twodimensional and of a threedimensional disturbance.
 Publication:

Associazione Italiana di Meccanica Teorica ed Applicata, Volume 4
 Pub Date:
 1974
 Bibcode:
 1974itaa....4....1C
 Keywords:

 Boundary Value Problems;
 Flow Stability;
 Laminar Flow;
 Parallel Plates;
 Two Dimensional Flow;
 Finite Element Method;
 Flow Velocity;
 Small Perturbation Flow;
 Viscous Fluids;
 Vorticity;
 Fluid Mechanics and Heat Transfer