Abstract
Problems on the stability of laminar flow such as Poiseulle flow and boundary layer flow are one of the most traditional problems in the field of fluid mechanics. Though stability of free-surface flow has been studied by a number of researchers, detailed instability diagram illustrating the growth rate of perturbation in the wavenumber-Reynolds number plane has not been obtained so far. In this paper, we perform linear stability analysis of free surface flow by the use of the spectral collocation method with the Chebyshev polynomials and obtain detailed instability diagrams. It is found that the instability diagrams of free-surface flow are characterized by complicated unstable domains compared with those of 2D Poiseulle flow and boundary layer flow.
