Decomposition methods in turbulence research

Institute of Thermomechanics AS CR, v.v.i., Dolejškova 5, Praha 8
uruba@it.cas.cz

Abstract

Nowadays we have the dynamical velocity vector field of turbulent flow at our disposal coming thanks advances of either mathematical simulation (DNS) or of experiment (time-resolved PIV). Unfortunately there is no standard method for analysis of such data describing complicated extended dynamical systems, which is characterized by excessive number of degrees of freedom. An overview of candidate methods convenient to spatiotemporal analysis for such systems is to be presented. Special attention will be paid to energetic methods including Proper Orthogonal Decomposition (POD) in regular and snapshot variants as well as the Bi-Orthogonal Decomposition (BOD) for joint space-time analysis. Then, stability analysis using Principal Oscillation Patterns (POPs) will be introduced. Finally, the Independent Component Analysis (ICA) method will be proposed for detection of coherent structures in turbulent flow-field defined by time-dependent velocity vector field. Principle and some practical aspects of the methods are to be shown. Special attention is to be paid to physical interpretation of outputs of the methods listed above.