Lumley introduced the POD method to the turbulence community as an objective means of identifying coherent structures in turbulent flows. The concept entails the mathematical projection of a candidate structure onto an instantaneous field and performing a maximization in the mean-square sense. The unbiased nature of the POD yields a complete basis set, when applied correctly, has made its use for the development of models and examination of turbulent flows popular. Since the modes are optimal in the mean-square sense, the models developed are typically low-dimensional in nature.

Use of the POD modes as the basis set for the development of a model makes it low-dimensional in nature because the POD represents most of the essential flow physics in a small set of modes. A model set of Ordinary Differential Equations (ODE) is derived by expanding the instantaneous field in the governing equations as the summation of the POD expansion coefficient times the eigenfunction and subsequently, projecting the results onto the empirically determined eigenfunctions using a Galerkin method. The resultant set of ODE’s describes the time dependence of the POD expansion coefficients. These coefficients can be reprojected onto the engenfunctions to recreate a time-series of the flow using the POD. Since only a few modes can be used to describe the whole flowfield, it is quite appealing for testing control strategies.

POD research at CRAFT Tech is mainly focused on the application of the methodology to variable-density or compressible flows. To this extent we demonstrate the method as applied to : (1) 2D low speed shear layer; (2) 3D turbulent boundary layer; and, (3) 2D supersonic cavity.