Decay of streaks and rolls in plane Couette–Poiseuille flow

Liu, Tao; Semin, Benoît; Klotz, Lukasz; Godoy-Diana, Ramiro; Wesfreid, José Eduardo; Mullin, T.

doi:10.1017/jfm.2021.89

Cited by 12 publications

(8 citation statements)

References 42 publications

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“…For decay, we show the decay of energy associated with the three velocity components of the flow, Ex,Ey,Ez Efalse(x,y,zfalse)≡1LxLyLz∫normalΩ12false(u2,v2,w2false) dx. Figure 11 a shows that the reactive pathway from A to scriptB0 is such that Ey decays most quickly, followed by Ez, followed by Ex so that the tube of reactive trajectories approaches scriptB0 almost tangent to the Ex axis. This ordering of decay of energy components has been reported previously [6,47]; here the 90% probability isosurface shows that almost every successful decay trajectory follows a similar path.…”

Section: Transition Pathwayssupporting

confidence: 87%

Extreme events in transitional turbulence

Gomé

Tuckerman

Barkley

2022

Phil. Trans. R. Soc. A.

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Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier–Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

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Section: Transition Pathwayssupporting

confidence: 87%

Extreme events in transitional turbulence

Gomé

Tuckerman

Barkley

2022

Phil. Trans. R. Soc. A.

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“…One finds velocity streaks contained mostly in u x as well as streamwise vortices ω x that can be observed through the component u z (they are the main contribution to this velocity component) [Hamilton et al, 1995]. Moreover it has been observed in models, simulations and experiments that decay of turbulence was much faster in streamwise vortices (or its proxies) than in velocity streaks [Rolland, 2018, Liu et al, 2020, Gomé et al, 2020. We will endeavour to discuss this observation in specifically computed collapse trajectories.…”

Section: Visualisation Of the Collapse Trajectoriesmentioning

confidence: 97%

“…We will endeavour to discuss this observation in specifically computed collapse trajectories. On the other hand, most experimental observations are performed by PIV using a plane parallel to the wall, thus capturing u x and u z in a x − z plane near the midgap [Liu et al, 2020, De Souza et al, 2020.…”

Section: Visualisation Of the Collapse Trajectoriesmentioning

confidence: 99%

“…Meanwhile transitional turbulence can exist at moderate Reynolds numbers, albeit transiently [Eckhardt et al, 2008, Schmiegel and Eckhardt, 1997, Bottin and Chaté, 1998. Meanwhile, turbulence can build up from laminar flow under a finite amplitude forcing [Wan and Yu, 2017, Rolland, 2018, Liu et al, 2020, or somewhat equivalently from a finite amplitude initial condition [Faisst and Eckhardt, 2003]. This gives a first type of multistability, where the transitional turbulence of plane Couette flow can collapse down to laminar flow under its own fluctuations, and go back to turbulence if it is forced.…”

Section: Introductionmentioning

confidence: 99%

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Collapse of transitional wall turbulence captured using a rare events algorithm

Rolland

2021

Preprint

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This text presents one of the first successful applications of a rare events method for the study of multistability in a turbulent flow without stochastic energy injection. The trajectories of collapse of turbulence in plane Couette flow, as well as their probability and rate of occurrence are systematically computed using Adaptive Multilevel Splitting (AMS). The AMS computations are performed in a system of size Lx × Lz = 24 × 18 at Reynolds number R = 370 with an acceleration by a factor O(10) with respect to DNS and in a system of size Lx × Lz = 36 × 27 at Reynolds number R = 377 with an acceleration by a factor O(10 3 ). The AMS results are validated with a comparison to DNS in the system of size Lx × Lz = 24 × 18. Visualisations in both systems indicate that turbulence collapses because the self sustaining process of turbulence fails locally. The streamwise vortices decay first in streamwise elongated holes, leaving streamwise invariant streamwise velocity tubes that experience viscous decay. These holes then extend in the spanwise direction. The examination of more than a thousand of trajectories in the (Ec,x = u 2x /2 d 3 x, Ec,y−z = (u 2 y /2 + u 2 z /2) d 3 x) plane in the system of size Lx × Lz = 24 × 18 confirms the faster decay of streamwise vortices and shows concentration of trajectory. This hints at an instanton phenomenology in the large size limit. The computation of turning point states, beyond which laminarisation is certain, confirms the hole formation scenario and shows that it is more pronounced in larger systems. Finally, the examination of non reactive trajectories, where a hole opens then closes, indicates that hole opening and closing are distinct processes. Both the vortices and the streaks reform concomitantly when the laminar holes close.

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“…Batchelor and Townsend performed decay experiments starting from the turbulent state to establish that viscous dissipation sets the time scale of the final decay [16]. Likewise this method is similar to that used in previous CMF experiments studying individual puffs [5] and in transitional plane Couette-Poiseuille flow [17], but now we use it for both CMF and CPG flows. Assuming that the higher Re turbulent state is universal in both CPG and CMF flows, for which there is numerical evidence [18], the initial conditions should be the same for both flows.…”

mentioning

confidence: 99%