Eigenvalue spectrum versus energy density spectrum in a mixing tank

The goal of this paper is to relate eigenvalue spectrum issued from POD to energy density spectrum. In the first part of this paper, eigenvalue spectrum issued from POD is plotted. Reconstruction of kinetic energy (KE) and dissipation rate of KE are discussed. 1D energy density spectrum is plotted for complete fluctuating velocity field. Different projections of fluctuating velocities on selected groups of eigenmodes are discussed. In the second part of this paper, 1D longitudinal EDS is reconstructed by the way of information entropy (Ogawa, 2007), as a new perspective. The maximum entropy method (MEM) is used to derive the energy density spectrum (versus wave number) in the inertial range of a turbulent flow.