Long-wave models of thin film fluid dynamics
  Centre manifold techniques are used to derive rationally a description of the dynamics of thin films of fluid. The derived model is based on the free-surface $\eta(x,t)$ and the vertically averaged horizontal velocity $\avu(x,t)$. The approach appears to converge well and has significant differences from conventional depth-averaged models. 
A.J. Roberts (University of Southern Queensland)