Self-similar, spatially localized structures in turbulent pipe flow from a data-driven wavelet decomposition
ORAL
Abstract
Within the chaotic flow field of wall-bounded turbulence, there exist structures that are coherent in space and time. Gaining a mechanistic understanding of wall-bounded turbulence necessitates characterizing these coherent structures. According to Townsend’s attached eddy hypothesis (AEH), these coherent structures are self-similar in the log layer. Subsequent models, such as the attached eddy model, propose these structures are also spatially localized.
The most popular method for representing coherent structures in a flow field is proper orthogonal decomposition (POD), which produces a set of energetically ordered basis elements derived from data; however, in statistically homogeneous directions, POD basis elements are Fourier modes, which are undesirable for representing spatially localized structures. On the other hand, a traditional wavelet decomposition (TWD) provides basis elements that are multiscale and spatially localized; however, the basis is not derived from data and has self-similarity built into it.
We combine features of POD and TWD to obtain data-driven wavelet decomposition (DDWD), which extracts energetic and spatially localized structures from data. We apply DDWD to turbulent pipe flow at a friction Reynolds number of 12,400. We find self-similar, spatially localized structures in the streamwise range of 40–450 wall units to 1 pipe radii and the wall-normal range of 350 wall units to 1 pipe radii, which is consistent with other studies.
The most popular method for representing coherent structures in a flow field is proper orthogonal decomposition (POD), which produces a set of energetically ordered basis elements derived from data; however, in statistically homogeneous directions, POD basis elements are Fourier modes, which are undesirable for representing spatially localized structures. On the other hand, a traditional wavelet decomposition (TWD) provides basis elements that are multiscale and spatially localized; however, the basis is not derived from data and has self-similarity built into it.
We combine features of POD and TWD to obtain data-driven wavelet decomposition (DDWD), which extracts energetic and spatially localized structures from data. We apply DDWD to turbulent pipe flow at a friction Reynolds number of 12,400. We find self-similar, spatially localized structures in the streamwise range of 40–450 wall units to 1 pipe radii and the wall-normal range of 350 wall units to 1 pipe radii, which is consistent with other studies.
*This work was supported by AFOSR FA9550-18-1-0174 and ONR N00014-18-1-2865 (Vannevar Bush Faculty Fellowship). The authors are grateful to Marcus Hultmark and Matthew K. Fu of Princeton University for use of the Superpipe data and helpful discussions. The authors additionally thank Kelly Y. Huang, Gabriel G. Katul, and Alexander J. Smits for helpful discussions.
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Publication: Guo A., Floryan, D., Graham, M. (2023). Self-similar, spatially localized structures in turbulent pipe flow from a data-driven wavelet decomposition (under review)
Presenters
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Alex Guo
- University of Wisconsin-Madison