Degeneracy of turbulent states in two-dimensional channel flow

Markeviciute, Vilda K.; Kerswell, Rich R.

doi:10.1017/jfm.2021.336

Cited by 5 publications

(7 citation statements)

References 28 publications

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“…where setting g = 0 recovers the usual y-independent applied pressure gradient −G(t). For this situation it is already known that there is bistability with two statistically steady states possible in 2D channel flow at Re = 36,300 [60]: a state which is statistically symmetric about the channel midplane -the symmetric state S -and another which is statistically asymmetric -the asymmetric state A: see Fig. 2(left).…”

Section: Applicationmentioning

confidence: 87%

“…is kept constant (unstarred/starred quantities are dimensionless/dimensional). Non-dimensionalizing the Navier-Stokes equations using h * , 3U * /2 (so Reynolds numbers based on the bulk speed and the laminar centreline speed U * c = 3U * /2 correspond [60]) and ρ * leads to…”

Section: Formulation: Channel Flowmentioning

confidence: 99%

“…with the latter two reflecting the presence of non-slip walls. Following earlier work [60,68], the length of the channel is set to 4 times its height (L x = 4), Re = 36,300 and computationally, 1024 Fourier modes are used to discretize in the x direction and 256 Chebyshev modes in y (see [60] for details). The streamwise body force is defined in terms of a profile function g(y) as follows…”

Section: Applicationmentioning

confidence: 99%

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

Markeviciute¹,

Kerswell²

2022

Preprint

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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.

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Section: Applicationmentioning

confidence: 87%

Section: Formulation: Channel Flowmentioning

confidence: 99%

Section: Applicationmentioning

confidence: 99%

See 1 more Smart Citation

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

Markeviciute¹,

Kerswell²

2022

Preprint

Self Cite

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show abstract

“…For this situation, it is already known that there is bistability with two statistically steady states possible in a 2-D channel flow at Re = 36 300 (Markeviciute & Kerswell 2021): a state that is statistically symmetric about the channel midplane -the symmetric state S -and another that is statistically asymmetric -the asymmetric state A; see figure 2(a).…”

Section: Applicationmentioning

confidence: 95%

“…Here is defined as in § 2.1 so that the conditions are imposed with the latter two reflecting the presence of non-slip walls. Following earlier work (Falkovich & Vladimirova 2018), the length of the channel is set to four times its height (), and, computationally, Fourier modes are used to discretize in the direction and Chebyshev modes in direction (see Markeviciute & Kerswell (2021) for details).…”

Section: Applicationmentioning

confidence: 99%

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

Markeviciute

Kerswell

2023

J. Fluid Mech.

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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 (OS) 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) that corresponds to the quasilinearized Navier–Stokes equations, we develop an extended OS analysis that also incorporates information about the fluctuation field. A more practical version of this – minimally extended OS analysis – 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 shear flows by including more information about the underlying flow in its predictions as well as for other flows with additional physics such as convection.

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Penetrative convection: heat transport with marginal stability assumption

Ding

Ouyang

2023

J. Fluid Mech.

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This paper investigates heat transport in penetrative convection with a marginally stable temporal-horizontal-averaged field or background field. Assuming that the background field is steady and is stabilised by the nonlinear perturbation terms, we obtain an eigenvalue problem with an unknown background temperature $\tau$ by truncating the nonlinear terms. Using a piecewise profile for $\tau$ , we derived an analytical scaling law for heat transport in penetrative convection as $Ra\rightarrow \infty$ : $Nu=(1/8)(1-T_M)^{5/3}Ra^{1/3}$ ( $Nu$ is the Nusselt number; $Ra$ is the Rayleigh number and $T_M$ corresponds to the temperature at which the density is maximal). A conditional lower bound on $Nu$ , under the marginal stability assumption, is then derived from a variational problem. All the solutions to the full system should deliver a higher heat flux than the lower bound if they satisfy the marginal stability assumption. However, data from the present direct numerical simulations and previous optimal steady solutions by Ding & Wu (J. Fluid Mech., vol. 920, 2021, A48) exhibit smaller $Nu$ than the lower bound at large $Ra$ , indicating that these averaged fields are over-stabilised by the nonlinear terms. To incorporate a more physically plausible constraint to bound heat transport, an alternative approach, i.e. the quasilinear approach is invoked which delivers the highest heat transport and agrees well with Veronis's assumption, i.e. $Nu\sim Ra^{1/3}$ (Astrophys. J., vol. 137, 1963, p. 641). Interestingly, the background temperature $\tau$ yielded by the quasilinear approach can be non-unique when instability is subcritical.

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Degeneracy of turbulent states in two-dimensional channel flow

Abstract: Abstract

Cited by 5 publications

References 28 publications

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

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

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

Penetrative convection: heat transport with marginal stability assumption

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