Closing the loop: nonlinear Taylor vortex flow through the lens of resolvent analysis

Barthel, Benedikt; Zhu, Xiaojue; McKeon, Beverley

doi:10.1017/jfm.2021.623

Cited by 5 publications

(5 citation statements)

References 41 publications

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“…This work uses Chebyshev differential matrix [34] to discretize the radial derivative operator in the MATLAB R2020b. It also validates the numerical data through setting 𝜂 = 0.714.…”

Section: Methodsmentioning

confidence: 99%

Particle motion in Taylor-Couette flow experiments

Wang,

Liu

2023

TNS

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This work investigates particle transportation Taylor-Couette Flow (TCF) experiments. We designed and built up the experimental set-up and then did two groups of experiments (S1 and S2). Small radius ratio () experiments (S1) focuses on the settling time t_set of a particle, which increases when Reynolds number (R) increases. The settling time within Taylor-Couette flow is larger than that in the still water due to horizontal motion of particle. To further understand the underlying flow mechanism of this increased t_set, we designed the large experiments (S2), which identify Taylor vortices (TVF) and spiral vortices (SPI) that trap the particle and thus increase t_set. In addition, linear stability analysis also predicts the wavelength of flow structures in the same order of experimental observation, although some deviation exists.

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“…This work uses Chebyshev differential matrix [34] to discretize the radial derivative operator in the MATLAB R2020b. It also validates the numerical data through setting 𝜂 = 0.714.…”

Section: Methodsmentioning

confidence: 99%

Particle motion in Taylor-Couette flow experiments

Wang,

Liu

2023

TNS

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“…Similar considerations impact the development of numerical methods (Bazilevs et al. 2007), self-consistent mean flow modelling (Meliga 2017) and resolvent analysis (Padovan, Otto & Rowley 2020; Rigas, Sipp & Colonius 2021; Barthel, Zhu & McKeon 2021; Barthel, Gomez & McKeon 2022).…”

Section: Introductionmentioning

confidence: 93%

Multiscale model reduction for incompressible flows

Callaham,

Loiseau,

Brunton

2023

J. Fluid Mech.

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We introduce a projection-based model reduction method that systematically accounts for nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The proposed method uses a separation of time scales between the resolved and subscale variables to derive a reduced-order model with cubic closure terms for the truncated modes, generalizing the classic Stuart–Landau equation. The leading-order cubic terms are determined by averaging out fast variables through a perturbation series approximation of the action of a stochastic Koopman operator. We show analytically that this multiscale closure model can capture both the effects of mean-flow deformation and the energy cascade before demonstrating improved stability and accuracy in models of chaotic lid-driven cavity flow and vortex pairing in a mixing layer. This approach to closure modelling establishes a general theory for the origin and role of cubic nonlinearities in low-dimensional models of incompressible flows.

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“…It has been shown, however, that the nonlinear forcing may have little to no overlap with the leading forcing mode [8,15,32] resulting in χ 1 ≪ χ p =1 . This nonalignment stems from the fact that the resolvent does not model well the inter-scale nonlinear transfer.…”

Section: Cess Eddy Viscosity Modelmentioning

confidence: 99%

On the use of eddy viscosity in resolvent analysis of turbulent channel flow

Symon¹,

Madhusudanan²,

Illingworth³

et al. 2022

Preprint

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The predictions of resolvent analysis for turbulent channel flow are evaluated for a friction Reynolds number of Reτ = 550. In addition to the standard resolvent operator where only the kinematic viscosity appears, a resolvent operator augmented with the Cess eddy viscosity profile is considered. Adding eddy viscosity significantly alters the low-rank behavior of the resolvent. Regardless of the wave speed selected, the eddy resolvent is low-rank for spanwise wavelengths of λ + y = 80 and λy/h = 3.5 in comparison to the standard resolvent whose low-rank behavior depends on the wave speed. The leading eddy resolvent modes are shown to have higher projections onto the leading mode from spectral proper orthogonal decomposition in comparison to standard resolvent modes. Neither analysis, however, reliably predicts the most energetic wave speed. The standard resolvent tends to overestimate it while the eddy resolvent underestimates it. For scales where the most energetic wave speed is underestimated, the eddy resolvent modes are energetic too close to the wall. The eddy resolvent does, however, correctly identify the most energetic wave speed and mode shapes for structures that are associated with the near-wall cycle or that are most energetic at z/h = ±0.5. It is argued that these types of structures are likely to be correctly predicted for any friction Reynolds number due to the inner and outer scaling of the Cess eddy viscosity profile. Finally, it is shown that the accuracy of eddy predictions relies on striking the right balance between positive and negative energy transfers. Even though the eddy viscosity primarily adds dissipation, its wall-normal gradient injects energy in the near-wall region, resulting in mode shapes that are "attached" to the wall. For some scales, however, the predicted positive energy transfer is too strong thus biasing structures towards the wall. The ability of the Cess eddy viscosity profile to model both positive and negative energy transfers suggests that it could be optimized for individual scales to provide better low-order models of turbulent channel flow.

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Closing the loop: nonlinear Taylor vortex flow through the lens of resolvent analysis

Abstract: Abstract

Cited by 5 publications

References 41 publications

Particle motion in Taylor-Couette flow experiments

Particle motion in Taylor-Couette flow experiments

Multiscale model reduction for incompressible flows

On the use of eddy viscosity in resolvent analysis of turbulent channel flow

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