Modelling fluid flows in thin domains

Tony Roberts

The flow of thin layers of a fluid is common in a large number of industrial and biological areas.  The development of accurate models is essential for a proper understanding of these flows.  We review the modelling of thin films of fluids, possibly contaminated with both insoluble and soluble surfactants, flowing over a curved substrate. The models for thicker films incorporate the dynamical effects of inertia.  Our work using centre manifold techniques can provide systematic estimates of the errors in any simulation.  The centre manifold approach has a clear modelling process and has the flexibility to readily incorporate the complex physical mechanisms seen in these fluid dynamics.  Indeed the power of the approach is used to derive, using the same basic algorithm, proposed models for large scale turbulent flow such as floods.