NUMERICAL STUDIES OF POINT PERTURBATIONS IN LAMINAR PLANE POISEUILLE MOTION

摘要

A finite-difference technique is developed to study the time-dependent, two-dimensional, isothermal flow of an incompressible, Newtonian fluid be¬tween infinite, parallel planes. A theoretical analysis of the convergence and stability of the difference scheme is presented. The method developed is used to determine the propagation of a disturbance in the flow regime by numerical integration, with respect to time and space, of the nonlinear equations of motion for the perturbed plane Poiseuille flow. Several test computations are carried out wherein a small, point, vorticity perturbation is introduced into an initially laminar flow field; the perturbation is introduced on the channel axis. Vorticity distributions in the neighborhood of the channel axis, following perturbation, are presented in graphical form; the effects of perturbation magnitude and Reynolds number on vorticity propagation are discussed in a qualitative manner for the cases studied.