Stability of plane Poiseuille flow of viscoelastic fluids with uniform cross flow

Abstract

The second order fluid model has been employed to study the instability phenomenon of the flow between the two parallel walls with uniform cross-flow. Several approximations have been utilized in order to render the system solvable. In this way the problem appears highly idealized, but still it has a feature characteristic of turbulence namely the motion normal to the walls. The primary profile is asymmetric and in presence of elasticity it may be stabilized or destabilized by cross-flow. As before in the present case also the instabilities occur for the positive values of the parameterΛ, that is, when the second normal stress difference is positive. For polymers the present analysis shows that they retain their drag reduction characteristic even to the extent of high dilution, which is the fact observed experimentally.