Linear-model-based estimation in wall turbulence: improved stochastic forcing and eddy viscosity terms

Gupta, Vikrant; Madhusudanan, Anagha; Wan, Minping; Illingworth, Simon J.; Juniper, Matthew P.

doi:10.1017/jfm.2021.671

Cited by 22 publications

(71 citation statements)

References 67 publications

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“…The drawback of this approach is that it requires sufficient data in order to compute the leading SPOD mode. As such, other approaches have modified the Cess profile using scaling arguments [41] or a stochastic approach to model background turbulence that can inject or dissipate energy of coherent waves [26]. Regardless of the approach selected, the Cess profile provides a good initial condition for optimizing an eddy viscosity or modeling the effect of nonlinear terms as done in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…A similar parameter was introduced by Ref. [41] to derive a scale-dependent eddy viscosity for linear estimation of a turbulent channel flow at Re τ = 2003. The first singular value σ 1 is plotted against c + in Fig.…”

Section: Frequency Responsementioning

confidence: 99%

“…Refs. [41,46], overpredict the strength of fluctuations in the near-wall region when measurements are known in the logarithmic region. The biased mode shapes are also consistent with Ref.…”

Section: Artificially Adjusting the Eddy Viscosity Gradientmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Frequency Responsementioning

confidence: 99%

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

Symon¹,

Madhusudanan²,

Illingworth³

et al. 2022

Preprint

Self Cite

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“…The eddy viscosity in the Cess model is independent of the length scales of turbulent eddies. Gupta et al (2021) proposed that the eddy viscosity should depend on the length scales of turbulent eddies as…”

Section: Comparison Of Sweeping-enhanced and Eddy-viscosity-enhanced ...mentioning

confidence: 99%

“…This approach significantly improved the consistency between the resolvent modes and SPOD modes. Gupta et al (2021) proposed that the eddy viscosity and forcing intensity depend on the wavelengths and wall distances. The wavelength dependence of the eddy viscosity causes the small-wavelength fluctuations to not be overdamped, while the wall-distance dependence of the forcing intensity leads to a wall-normal distribution of energy production similar to that of the DNS result.…”

Section: Introductionmentioning

confidence: 99%

Composition of resolvents enhanced by random sweeping for large-scale structures in turbulent channel flows

He²

2023

J. Fluid Mech.

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Composite sweeping-enhanced resolvents, referred to as the ${\boldsymbol {R}}_s^2$ model, are proposed to predict the space–time statistics of large-scale structures in turbulent channel flows. This model incorporates two key mechanisms: (i) eddy damping is introduced to represent random sweeping decorrelation caused by nonlinear forcing, leading to a sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$ ; and (ii) the sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$ is composited into its iterations ${\boldsymbol {R}}_s^2$ to yield non-zero Taylor time microscales. The resulting ${\boldsymbol {R}}_s^2$ model can correctly predict the frequency spectra and two-point cross-spectra of large-scale structures. This model is compared numerically with eddy-viscosity-enhanced resolvent models. The latter are designed to represent energy transfer instead for time decorrelation, and thus underpredict the characteristic decay time scales. The ${\boldsymbol {R}}_s^2$ model correctly yields the characteristic decay time scales in turbulent channel flows.

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Progress in physical modeling of compressible wall-bounded turbulent flows

Cheng,

Chen,

Zhu

et al. 2024

Acta Mech. Sin.

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Understanding, modeling and control of the high-speed wall-bounded transition and turbulence not only receive wide academic interests but also are vitally important for high-speed vehicle design and energy saving because transition and turbulence can induce significant surface drag and heat transfer. The high-speed flows share some fundamental similarities with the incompressible counterparts according to Morkovin’s hypothesis, but there are also significant distinctions resulting from multi-physics coupling with thermodynamics, shocks, high-enthalpy effects, and so on. In this paper, the recent advancements on the physics and modeling of high-speed wall-bounded transitional and turbulent flows are reviewed; most parts are covered by turbulence studies. For integrity of the physical process, we first briefly review the high-speed flow transition, with the main focus on aerodynamic heating mechanisms and passive control strategies for transition delay. Afterward, we summarize recent encouraging findings on turbulent mean flow scaling laws for streamwise velocity and temperature, based on which a series of unique wall models are constructed to improve the simulation accuracy. As one of the foundations for turbulence modeling, the research survey on turbulent structures is also included, with particular focus on the scaling and modeling of energy-containing motions in the logarithmic region of boundary layers. Besides, we review a variety of linear models for predicting wall-bounded turbulence, which have achieved a great success over the last two decades, though turbulence is generally believed to be highly nonlinear. In the end, we conclude the review and outline future works.

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Linear-model-based estimation in wall turbulence: improved stochastic forcing and eddy viscosity terms

Abstract: Abstract

Cited by 22 publications

References 67 publications

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

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

Composition of resolvents enhanced by random sweeping for large-scale structures in turbulent channel flows

Progress in physical modeling of compressible wall-bounded turbulent flows

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