Nonlinear Stability of Plane Poiseuille Flow of Viscoelastic Liquids

Abstract

The stability of plane Poiseuille flow to finite disturbances was studied for the second order fluid using the cascade (Stuart-Watson-Reynolds-Potter) method. The analysis was carried out for elasticity numbers up to 10−4. In this range the Deborah number based upon disturbance propagation is small and the second order fluid is a consistent constitutive approximation. In contrast to linear theory in this region, elasticity has a stabilizing effect on finite disturbances relative to the Newtonian liquid and the difference between stability behavior of Newtonian and slightly elastic liquids tends to disappear.