A self-sustaining process model of inertial layer dynamics in high Reynolds number turbulent wall flows

Chini, Gregory P.; Montemuro, Brandon; White, Christopher M.; Klewicki, Joseph

doi:10.1098/rsta.2016.0090

Cited by 12 publications

(23 citation statements)

References 41 publications

(80 reference statements)

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“…In the present theory, as in VWI analysis (see § 2), the streamwise-invariant rolls are sustained by the nonlinear self-interaction of a streamwise-varying instability (here termed a 'fluctuation') mode. Unlike VWI theory, however, the Rayleigh instability mode supported by the wall-normal inflection in the streamwise velocity has a streamwise wavelength commensurate with the thickness of the embedded shear layer; that is, the streamwise wavelength of the fluctuation is small compared to the scale of the rolls, a crucial refinement of our prior theory (Chini et al 2017). Moreover, as demonstrated in § 3, the instability mode is refracted and rendered three-dimensional (3-D) owing to the comparably slow spanwise variation in the thickness of the embedded VF that is caused by the roll-scale spanwise variation of the streak velocity.…”

Section: Introductionmentioning

confidence: 78%

“…Building on our earlier theoretical investigation (Chini et al 2017), we hypothesize that sufficiently strong large-scale counter-rotating streamwise rolls, having a diameter much greater than the VF thickness and stacked in the wall-normal direction, can differentially homogenize an imposed background shear flow. As shown in figure 3, the result is a pattern of UMZs and embedded internal shear layers (i.e.…”

Section: Introductionmentioning

confidence: 89%

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A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

et al. 2020

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Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 89%

A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

et al. 2020

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“…Given this nature, it is also possible to consider any other form of such a model as long as it correctly models the energetics described here. In this respect, it is finally worth mentioning the recent phenomenological modelling of coherent structures using the notions of the relative equilibrium (Chini, Montemuro, White & Klewicki 2017), and such a modelling effort may also take some benefit from the energy balance discussed here.…”

Section: Continuation To High Reynolds Numbers With Eddy Viscositymentioning

confidence: 99%

Exact coherent states of attached eddies in channel flow

2019

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A new set of exact coherent states in the form of a travelling wave is reported in plane channel flow. They are continued over a range in $Re$ from approximately $2600$ up to $30\,000$, an order of magnitude higher than those discovered in the transitional regime. This particular type of exact coherent states is found to be gradually more localised in the near-wall region on increasing the Reynolds number. As larger spanwise sizes $L_{z}^{+}$ are considered, these exact coherent states appear via a saddle-node bifurcation with a spanwise size of $L_{z}^{+}\simeq 50$ and their phase speed is found to be $c^{+}\simeq 11$ at all the Reynolds numbers considered. Computation of the eigenspectra shows that the time scale of the exact coherent states is given by $h/U_{cl}$ in channel flow at all Reynolds numbers, and it becomes equivalent to the viscous inner time scale for the exact coherent states in the limit of $Re\rightarrow \infty$. The exact coherent states at several different spanwise sizes are further continued to a higher Reynolds number, $Re=55\,000$, using the eddy-viscosity approach (Hwang & Cossu, Phys. Rev. Lett., vol. 105, 2010, 044505). It is found that the continued exact coherent states at different sizes are self-similar at the given Reynolds number. These observations suggest that, on increasing Reynolds number, new sets of self-sustaining coherent structures are born in the near-wall region. Near this onset, these structures scale in inner units, forming the near-wall self-sustaining structures. With further increase of Reynolds number, the structures that emerged at lower Reynolds numbers subsequently evolve into the self-sustaining structures in the logarithmic region at different length scales, forming a hierarchy of self-similar coherent structures as hypothesised by Townsend (i.e. attached eddy hypothesis). Finally, the energetics of turbulent flow is discussed for a consistent extension of these dynamical systems notions to high Reynolds numbers.

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“…In so doing, they show that nonlinear modulation phenomena are also important to the outer region flow structure: a structure nominally comprised of uniform zones of streamwise momentum segregated by slender regions of intense vorticity [31]. The physics of these interactions connect to a number of studies herein [11,12,19], but perhaps most directly to the asymptotic theory of Chini et al [32].…”

Section: Introductionmentioning

confidence: 99%

“…The precise mechanisms that sustain these spatially adjacent motions, however, are far from clear. Guided by the magnitude ordering of terms emerging from analysis of the mean equations, Chini et al [32] develop an asymptotically reduced, Navier-Stokes based theory that describes the interactions between a vortical fissure and the adjacent uniform momentum zones. Consistent with the perspectives of Cossu & Hwang [12], this model predicts that the coupled UMZ/VF structure is locally self-sustaining and, more specifically, that the driving turbulent stress divergence originates from a critical layer centred within the vortical fissure.…”

Section: (D) Asymptotically Reduced Modelsmentioning

confidence: 99%

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

Klewicki

Chini

Gibson

2017

Phil. Trans. R. Soc. A.

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Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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A self-sustaining process model of inertial layer dynamics in high Reynolds number turbulent wall flows

Cited by 12 publications

References 41 publications

A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

Exact coherent states of attached eddies in channel flow

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

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