Proper orthogonal decomposition and its applications

The proper orthogonal decomposition (POD) has become a very useful tool in the analysis and low-dimensional modelling of flows. It provides an objective way of identifying the ‘coherent’ structures in a turbulent flow. The application of POD to the case of a thermally driven two-dimensional flow of air in a horizontal rotating cylinder is presented. The data for the POD analysis are obtained by numerical integrations of the governing equations of mass, momentum and energy. The decomposition based on POD modes or eigenfunctions is shown to converge to within 5% deviation of the computational data for a maximum of 15 modes for the different cases. The presence of degenerate eigenvalues is an indicator of travelling waves in the flow, and this is confirmed by symmetry in both space and time for the corresponding eigenfunctions. Wave speeds are also determined for these travelling waves. Furthermore, low-dimensional models are constructed employing a Galerkin procedure. The low-dimensional models yield accurate qualitative as well as quantitative behaviour of the system. Not more than 20 modes are required in the low-dimensional models to accurately model the system dynamics. The ability of low-dimensional models to accurately predict the system behaviour for the set of parameters different from the one they were constructed from is also examined. Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.