PROPER ORTHOGONAL DECOMPOSITION APPLIED TO TURBULENT-FLOW IN A SQUAREDUCT

The proper orthogonal decomposition method is used to extract empirica l eigenfunctions from an incompressible turbulent flow in a square duc t. The two-dimensional eigenfunctions, corresponding to the two inhomo geneous duct directions, are optimal in the energy sense. The database used to form the two-point correlation tenser is obtained from a low Reynolds number direct numerical simulation of the flow field. The sym metries inherent in the square cross section allow the formulation of the integral eigenvalue problem over one octant, producing an eigensys tem of manageable size without losing any spatial scales. The extracti on process reveals a gradual decrease of modal energies rather than a single dominant eigenfunction. Reconstructions of instantaneous veloci ty fields and Reynolds stresses indicate the efficiency, as it pertain s to identifying structures and storing data, of the proper orthogonal decomposition method for this problem.