Low-dimensional representation of fluid flows using proper orthogonal decomposition

The fluid flow around a bluff body is complex and time dependent, which also contains a wide range of time and length scales. The first few eigenmodes of the proper orthogonal decomposition (POD) of such a flow provide significant insight into the flow structure, and can form the basis of a low-dimensional representation of certain turbulent flows. In this article, the direct-forcing immersed boundary method is considered to model the wake flow generated by arbitrary shaped obstacles. Based on the POD analysis of wakes behind cylinders, airfoils, and rotors, a reduced order model (ROM) for the prediction of wake dynamics is studied for arbitrary solid obstacles. For low Reynolds number time periodic flows, the POD based ROM accurately captures the statistically representative coherent motion. For high Reynolds number atmospheric boundary layer flow around rotors, POD provides a low-dimensional representation of the meaningful statistics of coherent motion. The POD based ROM is analyzed for turbulent flow past a rotor in the atmospheric boundary layer, where the flow is not periodic in time.