Cause-and-effect of linear mechanisms sustaining wall turbulence

Lozano-Durán, Adrián; Constantinou, Navid C.; Nikolaidis, Marios-Andreas; Karp, Michael

doi:10.1017/jfm.2020.902

Cited by 32 publications

(47 citation statements)

References 153 publications

(392 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this work, the GQL approximation in the streamwise direction has been applied to turbulent channel flow at Re τ ≈ 1700. In particular, this study aimed to examine the nonlinear interactions between the energy-containing streamwise waves, which have been understood to originate from the streak instability and/or transient growth mechanisms in the self-sustaining processes at different length scales (Park et al 2011;Alizard 2015;Cassinelli et al 2017;de Giovanetti et al 2017;Lozano-Durán et al 2021). This is a direct extension of previous studies of the QL model (Thomas et al 2014(Thomas et al , 2015Farrell et al 2016;Hernández & Hwang 2020) using the GQL approximation, as the QL model captures the dynamics of such energy-containing streamwise waves in a minimal manner with the linearised Navier-Stokes equations.…”

Section: Discussionmentioning

confidence: 99%

“…the lift-up effect) is captured, but the subsequent streak instability/transient growth and breakdown processes are approximated by the linearised equations about the streamwise-averaged velocity field. In fact, the mechanisms associated with streak instability and transient growth have been understood to play an important role in the determination of the streamwise length scales (Park et al 2011;Alizard 2015;Hwang 2015;Cassinelli et al 2017;de Giovanetti et al 2017;Lozano-Durán et al 2021). Despite being able to suitably resolve and/or model the key structural elements in the self-sustaining process, the size of which varies from the inner to the outer length scales, the following features indicate that the performance of the QL model may not be fully satisfactory (e.g.…”

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

confidence: 99%

“…For this purpose, the following two types of GQL approximations are considered in the present and the companion study (Hernández, Yang & Hwang 2021), respectively: (1) the low-wavenumber-mode group is given by the plane Fourier modes for |k x | ≤ k x,c (k x is the streamwise Fourier wavenumber and k x,c the corresponding threshold wavenumber for the decomposition) (present study); (2) the low-wavenumber-mode group is composed of the plane Fourier modes for |k z | ≤ k z,c (k z is the spanwise Fourier wavenumber and k z,c the corresponding threshold wavenumber for the decomposition) (Hernández et al 2021). The former case is to primarily examine the interactions between the energy-containing streamwise waves, which have been understood to originate from the streak instability and/or transient growth mechanisms in the self-sustaining processes at different length scales (Park, Hwang & Cossu 2011;Alizard 2015;Cassinelli, de Giovanetti & Hwang 2017;de Giovanetti, Sung & Hwang 2017;Lozano-Durán et al 2021), as well as the energy cascade in the streamwise wavenumber space. This is also a direct extension of the previous studies of the QL model (Thomas et al 2014(Thomas et al , 2015Farrell et al 2017;Pausch et al 2019;Hernández & Hwang 2020) using the GQL approximation, as the QL model offers the dynamics of such energy-containing streamwise waves in a minimal manner.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2022

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: Discussionmentioning

confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

2022

View full text Add to dashboard Cite

show abstract

“…U = U(y,z,t)x (e.g. see Table 1 of [51] for a sample list of relevant works). Despite this, the focus here is on the simplest mean flow definition U = U(y,t)x given the central role this plays in resolvent flow analysis but, there's no doubt, extending the mean flow definition is clearly an important direction to extend the approach discussed here.…”

Section: Introductionmentioning

confidence: 99%

Improved assessment of the statistical stability of turbulent flows using extended Orr-Sommerfeld stability analysis

Markeviciute¹,

Kerswell²

2022

Preprint

View full text Add to dashboard Cite

The concept of statistical stability is central to Malkus's 1956 attempt to predict the mean profile in shear flow turbulence. Here we discuss how his original attempt to assess this -an Orr-Sommerfeld analysis on the mean profile -can be improved by considering a cumulant expansion of the Navier-Stokes equations. Focusing on the simplest non-trivial closure (commonly referred to as CE2) which corresponds to the quasilinearized Navier-Stokes equations, we develop an extended Orr-Sommerfeld analysis (EOS) which also incorporates information about the fluctuation field. A more practical version of this -minimally extended Orr-Sommerfeld analysis (mEOS) -is identified and tested on a number of statistically-steady and therefore statistically stable turbulent channel flows. Beyond the concept of statistical stability, this extended stability analysis should also improve the popular approach of mean-flow linear analysis in time-dependent flows by including more information about the underlying flow in its predictions.

show abstract

“…Recently, Lozano-Durán, Bae & Encinar (2020) highlighted the importance of causal inference in fluid mechanics (see also Lozano-Durán et al 2021) and proposed to leverage information-theoretic metrics to explore causality in turbulent flows. In particular, Lozano-Durán et al (2020) examined the causal interactions of energy eddies in wall-bounded turbulence using transfer entropy.…”

Section: Introductionmentioning

confidence: 99%