Channel entrance flow and its linear stability

Abstract

In this work, we present a temporal linear stability analysis of developing channel flow. For the main flow, the considered solution is analytic. It is based on the hypothesis of small disturbances from fully developed flow and it is valid for intermediate Reynolds numbers. The disturbances are separated into symmetric and anti-symmetric eigenmodes of the velocity. We deal subsequently with the linear stability of this main flow, taking into account the nearly parallel flow assumption. The stability problem formulation leads to the Orr–Sommerfeld equation. This equation is then resolved using the Chebyshev spectral collocation method. The stability results depend essentially on the shape and amplitude of the velocity profiles imposed at the channel entry.