Spectral-POD Model for Large-Scale Structures in a Fully Developed Turbulent Channel Flow

An analytical procedure for extracting basis functions which approximate those given by POD method is developed. The cross-spectral tensor (S-ij) is determined from the solution of Fourier transformed two-point correlation equations. The obtained cross-spectral tensor is used to solve the POD eigenvalue problem. POD eigenfunctions and eigenvalues are then used to model the triple cross-spectral tensors (S-i,S-jk, S-ij,S-k) arisen in the spectral equations in an iterative manner. The mean velocity profile is used as model input and the spectral equations are solved for each pair of wave-numbers. A grid resolution equivalent to that of direct numerical simulation is used. The obtained basis functions are similar to POD eigenfunctions extracted from DNS data at the same Reynolds number.