Low dimensional POD-Galerkin modeling of rolling mode in a fully developed turbulent channel flow

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.

Low dimensional POD-Galerkin model is developed for a fully developed turbulent channel flow. This model is based on the extraction of the Proper Orthogonal Decomposition (POD) eigenfunctions from a DNS data set of a channel flow at Re¿ = 150. The POD eigenfunctions are optimal in energy sense and ordered with the first eigenfunction represents the most energetic structure. POD analysis shows that, POD mode 1, 2 and 3 capture 63 %, 18% and 8.5% of total kinetic energy, respectively. Stream-wise mode zero (stream-wise rolls) contains about 22% of total energy. A Galerkin projection is then used to drive dynamical systems. To investigate coherent structures near the wall in a low dimensional system, only energetic modes are considered. The coupling of stream-wise and wallnormal velocity components is sustained by the implicit coupling in the POD eigenfunctions. Statistics of the flow which is generated by the model compare fairly well with the corresponding POD reconstruction of DNS data from which POD basis are extracted.