A potential-based linear stability analysis of bilayer Couette and film flow with topography present

A new potential-based first-integral approach is proposed and formulated, facilitating the efficient generation of base-flow solutions for a particular class of bilayer Couette and film flows and a subsequent linear stability analysis of the same. A complicating feature of the flows investigated is the presence of surface topography. The methodology employed gives rise to (i) an advantageous dynamic boundary condition at a layer-separating interface or free-surface; (ii) base-flow solutions having a semi-analytic form; and (iii) the convenient mapping of the associated flow domains to regular rectangular counterparts. Typical base-flow results are provided for periodically repeating surface topography of differing amplitude. The novel stability analyses performed compare results obtained when surface topography is present with those for the corresponding benchmark case when surface topography is absent.