Scaling of turbulence intensities up to 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mtext>Re</mml:mtext><mml:mi>τ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>6</mml:mn></mml:msup></mml:mrow></mml:math>
 with a resolvent-based quasilinear approximation

Skouloudis, Nikolaos; Hwang, Yongyun

doi:10.1103/physrevfluids.6.034602

Cited by 17 publications

(25 citation statements)

References 77 publications

(228 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this respect, the QL model can further be improved from various perspectives: for example, in the context of the present QL/GQL models, λ x,c can further be considered as a function of λ z , or, alternatively, one can introduce energetically neutral stochastic forcing to enrich the dynamics. Indeed, the latter idea was central to the recent work by Hwang & Eckhardt (2020) and Skouloudis & Hwang (2021), where a minimal QL approximation, much simpler than the QL/GQL models in the present study, was shown to reproduce the key statistical behaviours, if the mean-fluctuation dynamics is captured with a suitable model for the self-interacting nonlinear term. In the context of the present QL/GQL models, λ x,c can further be considered as a function of λ z .…”

Section: Multi-scale Dynamics In the Ql And Gql Modelsmentioning

confidence: 81%

“…stochastic forcing, eddy viscosity, etc. ): for example, stochastic structural stability theory (Farrell & Ioannou 2003, 2007, 2012, direct statistical simulation (Marston, Conover & Tobias 2008;Tobias & Marston 2013), self-consistent approximation for linearly unstable flows (Mantič-Lugo, Arratia & Gallaire 2014;Mantič-Lugo & Gallaire 2016), minimal QL approximation augmented with an eddy-viscosity model (Hwang & Eckhardt 2020;Skouloudis & Hwang 2021), restricted nonlinear model (RNL) (Thomas et al 2014(Thomas et al , 2015Farrell, Gayme & Ioannou 2017;Pausch et al 2019;Hernández & Hwang 2020) and generalised quasilinear (GQL) approximations (Bakas & Ioannou 2013, 2014Bakas, Constantinou & Ioannou 2015;Constantinou 2015;Marston, Chini & Tobias 2016;Tobias & Marston 2017) in the context of atmospheric turbulence.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalised quasilinear approximations of turbulent channel flow. Part 1. Streamwise nonlinear energy transfer

2022

Self Cite

View full text Add to dashboard Cite

A generalised quasilinear (GQL) approximation (Marston et al., Phys. Rev. Lett., vol. 116, 2016, 104502) is applied to turbulent channel flow at $Re_\tau \simeq 1700$ ( $Re_\tau$ is the friction Reynolds number), with emphasis on the energy transfer in the streamwise wavenumber space. The flow is decomposed into low- and high-streamwise-wavenumber groups, the former of which is solved by considering the full nonlinear equations whereas the latter is obtained from the linearised equations around the former. The performance of the GQL approximation is subsequently compared with that of a QL model (Thomas et al., Phys. Fluids, vol. 26, 2014, 105112), in which the low-wavenumber group only contains zero streamwise wavenumber. It is found that the QL model exhibits a considerably reduced multi-scale behaviour at the given moderately high Reynolds number. This is improved significantly by the GQL approximation which incorporates only a few more streamwise Fourier modes into the low-wavenumber group, and it reasonably well recovers the distance-from-the-wall scaling in the turbulence statistics and spectra. Finally, it is proposed that the energy transfer from the low- to the high-wavenumber group in the GQL approximation, referred to as the ‘scattering’ mechanism, depends on the neutrally stable leading Lyapunov spectrum of the linearised equations for the high-wavenumber group. In particular, it is shown that if the threshold wavenumber distinguishing the two groups is sufficiently high, the scattering mechanism can be completely absent due to the linear nature of the equations for the high-wavenumber group.

show abstract

Section: Multi-scale Dynamics In the Ql And Gql Modelsmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Generalised quasilinear approximations of turbulent channel flow. Part 1. Streamwise nonlinear energy transfer

2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…2013; Hwang 2016; Hwang, Willis & Cossu 2016; McKeon 2017; Eckhardt & Zammert 2018; Doohan, Willis & Hwang 2019; McKeon 2019; Vadarevu et al. 2019; Yang, Willis & Hwang 2019; Hwang & Eckhardt 2020; Hwang & Lee 2020; Skouloudis & Hwang 2021).…”

Section: Introductionmentioning

confidence: 99%

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

2021

Self Cite

View full text Add to dashboard Cite

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

show abstract

“…As discussed in the cited paper, even with restricted wavenumbers and frequencies, such a superposition is non-unique, as there are several combinations of forcing modes that lead to the same overall Reynolds shear stress. While the approach of Skouloudis & Hwang (2021) leads to correct Reynolds number trends, a quantitative comparison with simulation data reveals differences. Information on nonlinear terms driving flow responses may be built into dynamic attached-eddy models for more accurate predictions.…”

Section: Introductionmentioning

confidence: 97%

“…A related effort is the work of Skouloudis & Hwang (2021), who superpose resolvent modes with various wavenumbers, as a representation of attached eddies, so as to recover the Reynolds shear stress of channels. This is referred to as a quasi-linear approximation (QLA), which may be seen as a dynamic model of attached eddies based on the linearised Navier-Stokes operator.…”

Section: Introductionmentioning

confidence: 99%

Self-similar mechanisms in wall turbulence studied using resolvent analysis

et al. 2022

View full text Add to dashboard Cite

Self-similarity of wall-attached coherent structures in a turbulent channel at $Re_\tau =543$ is explored by means of resolvent analysis. In this modelling framework, coherent structures are understood to arise as a response of the linearised mean-flow operator to generalised frequency-dependent Reynolds stresses, considered to act as an endogenous forcing. We assess the self-similarity of both the wall-attached flow structures and the associated forcing. The former are educed from direct numerical simulation data by finding the flow field correlated with the wall shear, whereas the latter is identified using a frequency space version of extended proper orthogonal decomposition (Borée, Exp. Fluids, vol. 35, issue 2, 2003, pp. 188–192). The forcing structures identified are compared to those obtained using the resolvent-based estimation introduced by Towne et al. (J. Fluid Mech., vol. 883, 2020, A17). The analysis reveals self-similarity of both wall-attached structures – in quantitative agreement with Townsend's hypothesis of self-similar attached eddies – and the underlying forcing, at least in certain components.

show abstract

Scaling of turbulence intensities up to Reτ=106 with a resolvent-based quasilinear approximation

Cited by 17 publications

References 77 publications

Generalised quasilinear approximations of turbulent channel flow. Part 1. Streamwise nonlinear energy transfer

Generalised quasilinear approximations of turbulent channel flow. Part 1. Streamwise nonlinear energy transfer

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

Self-similar mechanisms in wall turbulence studied using resolvent analysis

Contact Info

Product

Resources

About