Data-driven enhancement of coherent structure-based models for predicting instantaneous wall turbulence

Deshpande, Rahul; Silva, Charitha de; Lee, Myoungkyu; Monty, Jason; Marušić, Ivan

doi:10.1016/j.ijheatfluidflow.2021.108879

Cited by 11 publications

(24 citation statements)

References 58 publications

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“…By applying this novel method to multi-point datasets, understandings of the spatial coherence of the Fourier modes of wall-attached motions are significantly promoted (Chandran et al 2017;Baidya et al 2019;Deshpande et al 2019Deshpande et al , 2020Deshpande, Monty & Marusic 2021a). Furthermore, Baidya et al (2017), Eich et al (2020) and Deshpande et al (2021b) used Λ-shaped eddy packets to synthetically reconstruct statistical quantities of inertial motions in wall-bounded turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Statistical signatures of component wall-attached eddies in proper orthogonal decomposition modes of a turbulent boundary layer

et al. 2022

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Physical representation of coherent motions in wall-bounded turbulence satisfying Townsend's attached-eddy hypothesis (AEH) is still an open question to be debated. Here, we apply proper orthogonal decomposition (POD) to instantaneous snapshots of $u$ component velocity fields in the streamwise–wall-normal plane of three turbulent boundary layers, which cover a frictional Reynolds number ( $Re$ ) of $Re_\tau \approx 1000{\sim} 4000$ and were either measured by large-field-of-view planar particle image velocimetry or calculated by direct numerical simulation. The $u$ component POD modes characterized by streamwise recurring large-scale motions are decomposed into wall-attached and wall-detached parts depending on the wall-attachment condition. The former, i.e. wall-attached POD eddies, are believed to be the prime statistical representations of attached eddies. The reason lies in three aspects. Firstly, wall-attached POD eddies are geometrically self-similar and statistically independent. Secondly, the wall-normal variation of the variance of reduced-order streamwise velocity components $\tilde {u}_{AE}$ , which is only contributed by wall-attached POD eddies, presents logarithmic decay in the inertial flow region. Thirdly, analysis on the scaling behaviour of the high-even-order moment, moment generating function, as well as longitudinal two-point structure function, all indicate a quasi-Gaussian behaviour of $\tilde {u}_{AE}$ . None of these AEH-predicted behaviours are evident when the contribution of superstructure-like POD eddies are considered. Furthermore, wall-detached POD eddies are found to also present quasi-Gaussian behaviour. They might be treated as passive fragments of wall-attached ones.

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Section: Introductionmentioning

confidence: 99%

“…(2020) and Deshpande et al. (2021 b ) used -shaped eddy packets to synthetically reconstruct statistical quantities of inertial motions in wall-bounded turbulence.…”

Section: Introductionmentioning

confidence: 99%

Statistical signatures of component wall-attached eddies in proper orthogonal decomposition modes of a turbulent boundary layer

et al. 2022

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“…Their estimates, however, were limited to two-point velocity correlations reconstructed in a particular wall-parallel plane, which cannot be uniquely associated with the LSMs responsible for the superstructure formation (Deshpande et al 2020). Considering that superstructures extend down from the log-region to the wall, Deshpande et al (2021b) reconstructed two-point velocity correlations across two wall-parallel planes located in the near-wall and the log-region. These statistics, which are purely representative of the large 'wall-coherent' motions, revealed similar spanwise extents of the coexisting superstructures and LSMs for all canonical wall flows, thereby favouring the concatenation argument.…”

Section: Introductionmentioning

confidence: 99%

“…This has also led to growing acceptance of the existence of the geometrically self-similar attached eddy hierarchy in the inertial region (de Silva et al 2016;Baars et al 2017;Hwang & Sung 2018;Hu et al 2020;Deshpande et al 2020Deshpande et al , 2021a, which can be modelled conceptually . These advancements make it compelling to investigate whether these self-similar inertial motions are associated with the formation of superstructures, a conjecture that has previously shown promising results when implemented in coherent structure-based models (Chandran et al 2020;Deshpande et al 2021b). If this conjecture is proven true, then the preferred streamwise alignment of this energy-containing hierarchy of motions (to form superstructures) would have implications on Townsend's attached eddy hypothesis, which otherwise assumes a random distribution of attached eddies in the flow field (Townsend 1976;.…”

Section: Introductionmentioning

confidence: 99%

Evidence that turbulent superstructures are concatenations of geometrically self-similar coherent motions

Deshpande¹,

Silva²,

Marušić³

2022

Preprint

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We present evidence suggesting that the superstructures in turbulent boundary layers are concatenations of smaller, geometrically self-similar coherent motions. The evidence comes from identifying and analyzing instantaneous superstructures from large-scale particle image velocimetry datasets, capable of capturing streamwise elongated motions extending up to 12 times the boundary layer thickness. Given the challenge in identifying the constituent motions of the superstructures based on streamwise velocity signatures, an approach is adopted that investigates the wall-normal velocity fluctuations within these very long motions, which reveals the constituent motions unambiguously. The conditional streamwise energy spectra of the wall-normal fluctuations, corresponding exclusively to the superstructure region, are found to exhibit the well-known distance-from-the-wall scaling in the intermediate scale range. This indicates geometrically self-similar motions co-exist within the superstructures. The same spectra also exhibit a unique energy enhancement at the large scales, suggesting the spatial organization of self-similar motions (i.e. concatenation) over extended streamwise distances, which plausibly leads to the appearance of superstructures. This interpretation is also confirmed by analyzing synthetically generated flow fields comprising self-similar structures. The association of the superstructures with the self-similar motions is further reinforced by computing conditionally averaged two-point correlations, representing the vertical coherence of the constituent motions, which are found to match with the mean correlations. The mean vertical coherence of the Reynolds-shear-stress carrying motions, which is investigated for the log-region across three decades of Reynolds numbers, is found to exhibit universal distance-from-the-wall scaling. The findings support the prospect for modelling these dynamically significant motions via data-driven coherent structure-based models.

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“…This line of research has focused on analysis of data recorded from system dynamics to reveal much of the desired properties of the system at hand. Examples include data-driven identification of transfer operators and their eigenvalues, eigenfunctions and eigenmodes [ 31 , 32 ], data-driven identification of coherent structures in dynamical systems [ 33 – 38 ], and bifurcation forecasting methods for data-driven nonlinear stability analysis of dynamical systems [ 39 – 44 ].…”

Section: Introductionmentioning

confidence: 99%

Data-driven prediction in dynamical systems: recent developments

Ghadami

Epureanu

2022

Phil. Trans. R. Soc. A.

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In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

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Data-driven enhancement of coherent structure-based models for predicting instantaneous wall turbulence

Cited by 11 publications

References 58 publications

Statistical signatures of component wall-attached eddies in proper orthogonal decomposition modes of a turbulent boundary layer

Statistical signatures of component wall-attached eddies in proper orthogonal decomposition modes of a turbulent boundary layer

Evidence that turbulent superstructures are concatenations of geometrically self-similar coherent motions

Data-driven prediction in dynamical systems: recent developments

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