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.
