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Couette flow with geometrically induced unsteady effects

Film flow over surfaces containing topography is a key feature of a number of coating technologies. To date, detailed theoretical investigations of the same, underpinned by the long‐wave approximation, have been used to study the nature of the associated free‐surface disturbance formed; the internal flow structure being more‐or‐less of secondary importance. In the work reported here, a recently developed approach is used to explore the internal flow, embodying unsteady effects, for a related model problem in which the free‐surface is replaced by a moving upper boundary with its own topographical profile.