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Quasi-bivariate variational mode decomposition as a tool of scale analysis in wall-bounded turbulence

Abstract

The identification and separation of multi-scale coherent structures is a critical task for the study of scale interaction in wall-bounded turbulence. Here, we propose a quasi-bivariate variational mode decomposition (QB-VMD) method to extract structures with various scales from instantaneous two-dimensional (2D) velocity field which has only one primary dimension. This method is developed from the one-dimensional VMD algorithm proposed by Dragomiretskiy and Zosso (IEEE Trans Signal Process 62:531–544, 2014) to cope with a quasi-2D scenario. It poses the feature of length-scale bandwidth constraint along the decomposed dimension, together with the central frequency re-balancing along the non-decomposed dimension. The feasibility of this method is tested on both a synthetic flow field and a turbulent boundary layer at moderate Reynolds number (\(Re_{\tau }\) = 3458) measured by 2D particle image velocimetry (PIV). Some other popular scale separation tools, including pseudo-bi-dimensional empirical mode decomposition (PB-EMD), bi-dimensional EMD (B-EMD) and proper orthogonal decomposition (POD), are also tested for comparison. Among all these methods, QB-VMD shows advantages in both scale characterization and energy recovery. More importantly, the mode mixing problem, which degrades the performance of EMD-based methods, is avoided or minimized in QB-VMD. Finally, QB-VMD analysis of the wall-parallel plane in the log layer (at \(y/\delta\) = 0.12) of the studied turbulent boundary layer shows the coexistence of large- or very large-scale motions (LSMs or VLSMs) and inner-scaled structures, which can be fully decomposed in both physical and spectral domains.

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Acknowledgements

This work was supported by both the National Natural Science Foundation of China (Grant Nos. 11372001, 11672020 and 11490552) and the Fundamental Research Funds for the Central Universities of China (No. YWF-16-JCTD-A-05).

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Correspondence to Chong Pan.

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Wang, W., Pan, C. & Wang, J. Quasi-bivariate variational mode decomposition as a tool of scale analysis in wall-bounded turbulence. Exp Fluids 59, 1 (2018). https://doi.org/10.1007/s00348-017-2450-7

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