Characteristic-eddy decomposition of turbulence in a channel

Lumley's proper orthogonal decomposition technique is applied to the turbulent flow in a channel. Coherent structures are extracted by decomposing the velocity field into characteristic eddies with random coefficients. A generalization of the shot-noise expansion is used to determine the characteristic eddies in homogeneous spatial directions. Three different techniques are used to determine the phases of the Fourier coefficients in the expansion: (1) one based on the bispectrum, (2) a spatial compactness requirement, and (3) a functional continuity argument. Similar results are found from each of these techniques.