Dynamics of the Wavy Film Down an Inclined Plane. V. Newtonian Orr-Sommerfeld Problem Revisited

Linear stability of the Newtonian film flow along an inclined plate is studied by treating the related 2D linearized equations of fluctuating motion (Orr-Sommerfeld). Quadratic character of the Orr-Sommerfeld (OS) equations and the corresponding multiplicity of solution (the regular and singular branch) is demonstrated. Region of validity of both the long-wave (20 terms) and short-wave (4 terms) analytic asymptotes to the regular branch is estimated by comparing it with numerical solution to the full Orr-Sommerfeld problem. In particular, the c1-stability criterion of the regular long-wave asymptote is confirmed. In addition to the basic wave characteristics of the inception region (celerity, growth rate, wavelength), the characteristics of the fluctuating wall shear rate are given