  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.
