Linear stability of channel entrance flow

The spatial stability analysis of two dimensional, steady channel flow is investigated in the downstream entry zone. A model based on previous work, is presented for the base flow, which represents a small deformation of plane Poiseuille flow. The base flow evolution towards the fully developed state comes from the experimental and theoretical study of M. Asai and J.M. Floryan ”Certain aspects of channel entrance flow”, Phys. Fluids 16 (2004). This flow is found to be more stable than the parabolic Poiseuille flow, both when exponentially and algebraically growing disturbances are examined. The most destabilizing base flow defect is calculated using a variational method. The compromise between the destabilising effect of the defect, which diffuses downstream, and the instability growth is found to be insufficient to provoke transition in the downstream laminar flow.