Stability of Poiseuille flow of an incompressible second-grade Rivlin-Ericksen fluid

In the present work, the stability of Poiseuille flow of a second-grade incompressible Rivlin-Ericksen fluid in a circular cylinder is investigated by employing a linear analysis for cross sectional perturbations imposed on the known base flow. The perturbations were expanded in Fourier modes in the circumferential direction. This well-known method has been used for several classical problems in hydrodynamic stability, such as the Rayleigh-Taylor, Kelvin-Helmholtz and Taylor-Couette problems.