Stochastic linear modes in a turbulent channel flow

Tissot, Gilles; Cavalieri, André V. G.; Mémin, Étienne

doi:10.1017/jfm.2020.1168

Cited by 12 publications

(5 citation statements)

References 67 publications

(87 reference statements)

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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%

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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%

“…They did not, however, consider the improvements that could be achieved by adding an eddy viscosity model as done by Ref. [26].…”

Section: Introductionmentioning

confidence: 99%

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

Symon¹,

Madhusudanan²,

Illingworth³

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…Olson has employed a similar approach where a stochastic model of a turbulent fluid feeds the differential equation of convection-dispersion to study the effect of fiber length on particle dispersion [12]. Tissot and Cavalieri proposed a stochastic formulation of the Navier-Stokes equations to study the propagation of coherent structures within a turbulent channel flow [13]. Vianna and Nichele proposed a stochastic model to represent the annular flow in a tubular reactor followed by a numerical simulation to generate sample paths fitting the residence time distributions [14].…”

Section: Introductionmentioning

confidence: 99%

Measuring Turbulent Flows: Analyzing a Stochastic Process with Stochastic Tools

Rozos,

Wieland,

Leandro

2024

Fluids

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Assessing drag force and Reynolds stresses in turbulent flows is crucial for evaluating the stability and longevity of hydraulic structures. Yet, this task is challenging due to the complex nature of turbulent flows. To address this, physical models are often employed. Nonetheless, this practice is associated with difficulties, especially in the case of high sampling frequency where the inherent randomness of velocity fluctuations becomes mixed with the measurement noise. This study introduces a stochastic approach, which aims to mitigate bias from measurement errors and provide a probabilistic estimate of extreme stress values. To accomplish this, a simple experimental setup with a hydraulic jump was employed to acquire long-duration velocity measurements. Subsequently, a modified first-order autoregressive model was applied through ensemble simulations, demonstrating the benefits of the stochastic approach. The analysis highlights its effectiveness in estimating the uncertainty of extreme events frequency and minimizing the bias induced by the noise in the high-magnitude velocity measurements and by the limited length of observations. These findings contribute to advancing our understanding of turbulent flow analysis and have implications for the design and assessment of hydraulic structures.

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“…In recent years, the use of linear models to understand the physics that drive turbulent wall-bounded flows became widespread. Linear models provide a simple framework to work with and the emergency of tools such as resolvent analysis enables modeling coherent structures and self-sustaining mechanisms in flows [11][12][13][14][15][16]. In the resolvent framework the Navier-Stokes system is written in the state-space form, and the nonlinear terms are interpreted as external forcing terms [17][18][19][20], hence providing a convenient input-output formulation, relating the flow response and the forcing modes, related to non-linear terms in the Navier-Stokes system.…”

Section: Introductionmentioning

confidence: 99%

LES-informed resolvent-based estimation of turbulent pipe flow

Amaral¹,

Cavalieri²

2023

Preprint

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A resolvent-based methodology is employed to obtain spatio-temporal estimates of turbulent pipe flow from low-rank probe measurements of wall shear-stress fluctuations. Direct numerical simulations (DNS) and large-eddy simulations (LES) of turbulent pipe flow at friction Reynolds number of 550 are used as databases. We consider a DNS database as the true spatio-temporal flow field, from which wall shear-stress fluctuations are extracted and considered as measurements. A resolvent-based estimator is built following our earlier work (Amaral et al. J. Fluid Mech., vol. 927, 2021, p. A17), requiring a model for the nonlinear (or forcing) terms of the Navier-Stokes equations system, which are obtained from another DNS database, as in our earlier work, and from a series of computationally cheaper LES databases with coarser grids; the underlying idea is that LES may provide accurate statistics of non-linear terms related to large-scale structures at a low computational cost. Comparisons between the DNS and the estimates indicate that sufficiently accurate results can be achieved with estimators built with statistics from LES with an order of magnitude less grid points than the DNS, with estimates closely matching the reference DNS results up to the buffer layer and reasonable agreement up to the beginning of the log layer.

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Stochastic linear modes in a turbulent channel flow

Abstract: Abstract

Cited by 12 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

Measuring Turbulent Flows: Analyzing a Stochastic Process with Stochastic Tools

LES-informed resolvent-based estimation of turbulent pipe flow

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