Eigenvalue sensitivity to base flow variations in hagen-poiseuille flow

Transition in a cylindrical pipe flow still eludes thorough understanding. Most recent advances are based on the concept of transient growth of disturbances, but even this scenario is not fully confirmed by DNS and/or experiments. Based on the fact that even the most carefully conducted experiment is biased by uncertainties, we explore the spatial growth of disturbances developing on top of an almost ideal, axially invariant Poiseuille flow. The optimal deviation of the base flow from the ideal parabolic profile is computed by a variational technique, and unstable modes, driven by an inviscid mechanism, are found to exist for very small values of the norm of the deviation, at low Reynolds numbers.