A hybridized snapshot proper orthogonal decomposition-discrete wavelet transform technique for the analysis of flow structures and their time evolution

Abstract

A novel hybrid technique has been proposed in order to reveal in a greater detail the turbulent flow structures and their time evolution, and to address the issues and limitations related to the application of snapshot proper orthogonal decomposition (POD) and wavelet transform technique. The proposed hybrid technique combines the inherent abilities of the snapshot proper orthogonal decomposition and the two-dimensional discrete wavelet transform technique. The POD gives us the overall view of the most energetic flow pattern in an ensemble by decomposing the flow field into spatial and temporal modes, while two-dimensional wavelet transform gives us the localized spatial information through scale wise decomposition of the flow field. In this work, we apply the wavelet transform on the POD spatial modes. This enables us to understand the space scale structure of the flow events captured by the spatial POD modes, and the scale wise selectivity of these spatial POD modes. Thus, we are able to relate the most energetic flow events over a period of time (as obtained in spatial modes of snapshot POD) with the localized dominant scales that are contributing to it. Further, this information is utilized in the selection of those pod spatial modes that can effectively reconstruct a flow structure and its time evolution. The proposed technique has also been able to address the issues in the literature concerning the application of POD when the flow is less deterministic, as then a single POD mode may not reveal the flow structure and combination of modes is required to reconstruct it. In the present work, this hybrid methodology has been used to reveal the near wall intermittent events in channel flow: the ascending streaks and the bursts and their time evolution, the vortex tube and leading edge vortices in jet and the Taylor-Couette and irregular small chaotic vortices in Taylor-Couette flow. The planar dataset used for such an analysis has been obtained from particle image velocimetry and large eddy simulation studies.