Low-dimensional descriptions of turbulent flows: Experiment and modeling

Physics based low dimensional approaches are playing an increasingly important role in our understanding of turbulent flows. They provide an avenue for us to understand the connection between coherent structures and the overall dynamics of the flow field. As such these approaches are fundamental to the implementation of physics based active control methodologies. In this paper we present applications of the Proper Orthogonal Decomposition (POD) and Linear Stochastic Estimation (LSE), the physics based low dimensional approaches that we have been using over the past several years, to both the axisymmetric jet and the axisymmetric sudden expansion. For the high Reynolds number incompressible axisymmetric jet we demonstrate, from both low dimensional models and experimental low dimensional descriptions, that the dynamics can be described with relatively low dimensional information (1. POD mode and 5 or 6 azimuthal modes). We also show exciting recent experimental low dimensional results that suggest that the compressible jet (Mach numbers of 0.3 and 0.6) exhibit a similar low dimensional character. For the axisymmetric sudden expansion we use an LSE based low dimensional approach to demonstrate the large-scale unsteadiness of the reattachment region. We conclude with recent experimental results, which show how this large-scale unsteadiness leads to a very low dimensional character for this flow. Specifically, we And from the POD based experimental low dimensional description that the m=l azimuthal mode dominates throughout the flow field which has exciting implications for active flow control applications in such separated flows.