A unified well-posed computational approach for the 2D Orr–Sommerfeld problem

In this paper, we present a unified well-posed implicit formulation for nonlinear 2D Orr–Sommerfeld equation (OSE) enabling straightforward, efficient computation of travelling wave and steady solutions. We illustrate the ease and utility of our approach by computing classical travelling wave results of planar Poiseuille flows and novel steady solutions of the perturbed planar Couette flow, employing the path-following software AUTO.