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This research monograph gives a detailed review of the state-of-the-art theoretical analytical and numerical methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability representing an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion and more general for the understanding of the specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiments is illustrated and as a further bridge between the two the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of the underlying basic physics.§The monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program; researchers working on both applied and fundamental theoretical and experimental aspects of thin film flows; engineers and technologists dealing with processes involving at some stage thin films, either isothermal or heated. The monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.This research monograph gives a detailed review of the state-of-the-art theoretical analytical and numerical methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability representing an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion and more general for the understanding of the specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiments is illustrated and as a further bridge between the two the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of the underlying basic physics.§The monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program; researchers working on both applied and fundamental theoretical and experimental aspects of thin film flows; engineers and technologists dealing with processes involving at some stage thin films, either isothermal or heated. The monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.
