Low-order modelling of inertial instabilities in thick film flows

The expected ranges of applicability of low-order models of film flows have typically been quite restrictive; indeed, for many years good agreement with experiments and numerics was only found for thin films at zero Reynolds numbers. Ruyer-Quil and Manneville have demonstrated that a weighted residual technique can relieve the latter constraint for thin films, while Wray, Papageorgiou and Matar demonstrated that the former can be relaxed at zero Reynolds number. We combine these approaches to investigate the accuracy of low-order models for thick films with moderate levels of inertia, including validation against direct numerical simulations.