Monotonic energy stability for inclined laminar flows

The stability of planar shear flows of an incompressible fluid is fundamental and still a debated topic. In this article we define a family of basic flows which include Couette flow and Poiseuille flow, and use analytical methods and a Chebyshev collocation method with many different approaches to investigate the monotonic behaviour of the energy along perturbations. We obtain in different ways an extension of known results for general shear flows, and we confirm the validity of some approaches that can be found in the literature.