Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

Gomé, S.; Tuckerman, Laurette S.; Barkley, D.

doi:10.1017/jfm.2023.289

Cited by 4 publications

(1 citation statement)

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“…In analogy to pipe flow it has been suggested by Samanta et al (2011) that also in this two-dimensional setting the finite width of stripes is related to the energy depletion of the mean velocity profile and therefore the apparent wavelength of stripe patterns is set by local interactions and not by some global instability (Prigent et al 2002). Recently, the mechanism of wavelength selection in Couette flow has been associated by Gomé, Tuckerman & Barkley (2023) with an energy maximization principle of the large-scale circulatory flow surrounding stripes. In the present study we focus on isolated stripes (see figure 1) which already appear at somewhat lower Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows

Marensi,

Yalnız,

Hof

2023

J. Fluid Mech.

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The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.

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Section: Introductionmentioning

confidence: 99%

Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows

Marensi,

Yalnız,

Hof

2023

J. Fluid Mech.

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Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction

2023

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Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of spatially intermittent turbulent structures. In plane shear flows, these appear as a regular pattern of alternating turbulent and quasi-laminar flow. Both the physical and the spectral energy balance of a turbulent–laminar pattern in plane Couette flow are computed and compared to those of uniform turbulence. In the patterned state, the mean flow is strongly modulated and is fuelled by two mechanisms: primarily, the nonlinear self-interaction of the mean flow (via mean advection), and secondly, the extraction of energy from turbulent fluctuations (via negative spectral production, associated with an energy transfer from small to large scales). Negative production at large scales is also found in the uniformly turbulent state. Important features of the energy budgets are surveyed as a function of $Re$ through the transition between uniform turbulence and turbulent–laminar patterns.

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Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

2023

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Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of oblique, spatially intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a spatio-temporal intermittent process in which localised quasi-laminar gaps randomly nucleate and disappear. For slightly lower Reynolds numbers, spatially periodic and approximately stationary turbulent–laminar patterns predominate. The statistics of quasi-laminar regions, including the distributions of space and time scales and their Reynolds-number dependence, are analysed. A smooth, but marked transition is observed between uniform turbulence and flow with intermittent quasi-laminar gaps, whereas the transition from gaps to regular patterns is more gradual. Wavelength selection in these patterns is analysed via numerical simulations in oblique domains of various sizes. Via lifetime measurements in minimal domains, and a wavelet-based analysis of wavelength predominance in a large domain, we quantify the existence and nonlinear stability of a pattern as a function of wavelength and Reynolds number. We report that the preferred wavelength maximises the energy and dissipation of the large-scale flow along laminar–turbulent interfaces. This optimal behaviour is due primarily to the advective nature of the large-scale flow, with turbulent fluctuations playing only a secondary role.

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Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

Cited by 4 publications

References 68 publications

Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows

Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows

Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction

Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelength

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