Proper orthogonal decomposition applied to turbulent flow in a square duct

Publisher Website
Google Scholar
Abstract
The proper orthogonal decomposition method is used to extract empirical eigenfunctions from an incompressible turbulent flow in a square duct. The two-dimensional eigenfunctions, corresponding to the two inhomogeneous duct directions, are optimal in the energy sense. The database used to form the two-point correlation tensor is obtained from a low Reynolds number direct numerical simulation of the flow field. The symmetries inherent in the square cross section allow the formulation of the integral eigenvalue problem over one octant, producing an eigensystem of manageable size without losing any spatial scales. The extraction process reveals a gradual decrease of modal energies rather than a single dominant eigenfunction. Reconstructions of instantaneous velocity fields and Reynolds stresses indicate the efficiency, as it pertains to identifying structures and storing data, of the proper orthogonal decomposition method for this problem.