Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers

Goto, Susumu; Saito, Yuta; Kawahara, Genta

doi:10.1103/physrevfluids.2.064603

Cited by 68 publications

(152 citation statements)

References 56 publications

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“…Conclusion We have presented a UPO in turbulent LES and have demonstrated that, although the intertial range is narrow, the periodic dynamics bear the hallmarks of the energy cascade process: a time delay between the maxima of energy input, transfer at intermediate scales and dissipation; spatial intermittency and the −5/3 scaling in the energy spectrum. The vortical dynamics observed in the UPO, and their overlap with energy transfer events, are consistent with the scenario proposed by Melander & Hussain [4] and investigated in detail by Goto et al [8].…”

Section: Les Of Box Turbulencesupporting

confidence: 90%

Time-Periodic Inertial Range Dynamics

Vela-Martín

Kawahara

2019

Phys. Rev. Lett.

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We present an unstable periodic orbit in large eddy simulation of an incompressible fluid in a periodic box subject to a constant body force. The width of the inertial range of spatial scales, on which this simulation models high-Reynolds-number turbulence, is about three quarters of a decade, and a significant −5/3 scaling range is observed. We identify events of intense energy transfer across spatial scales and relate them to vortical dynamics.

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Section: Les Of Box Turbulencesupporting

confidence: 90%

Time-Periodic Inertial Range Dynamics

Vela-Martín

Kawahara

2019

Phys. Rev. Lett.

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“…These observations coincide with recent works by Goto et al, which numerically demonstrate the existence of a hierarchy of perpendicular vortex filaments emerging from larger counter-rotating vortices in both fully developed homogeneous isotropic turbulence and wallbounded turbulence [31][32][33]. This hierarchy of counterrotating perpendicular filaments, which arise from the interactions of larger parent vortices, appear over four distinct scales in Goto's simulations [32]. Due to the striking similarities between the iterative mechanism we observe and the results of Goto, we propose that the elliptical instability is likely the means by which these iterative generations of perpendicular filaments are formed.…”

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confidence: 91%

Turbulence generation through an iterative cascade of the elliptical instability

et al. 2020

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The essence of turbulent flow is the conveyance of kinetic energy through the formation, interaction, and destruction of eddies over a wide range of spatial scalesfrom the largest scales where energy is injected, down to the smallest scales where it is dissipated through viscosity. For nearly a century, this universal energy cascade has been the foundation of our understanding for how turbulent flows function. However, a mechanistic description of how ensembles of vortices interact to drive this energy cascade remains elusive. Here we introduce one essential mechanism for turbulence. We show that a sequence of the elliptical instability, arising from the close interaction between counter-rotating vortices, leads to the emergence of turbulent flow. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments, which are perpendicular to the original vortex tubes. These secondary filaments interact with one another, leading to the generation of even smaller tertiary filaments. This iterated cascade of the elliptical instability produces vortices of smaller and smaller sizes, until viscosity damps out all motion. In our experiments and simulations, we clearly observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be a fundamental mechanism by which the turbulent cascade develops and is sustained.

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“…A vast body of literature places vortex stretching at the core of the energy transfer mechanism among scales (Leung et al 2012;Goto et al 2017;Lozano-Durán et al 2016;Motoori & Goto 2019), while recent works suggest that strain-rate self-amplification is the main contributor to the energy transfer (Carbone & Bragg 2019). Thus, it is relevant to explore the connection between the flow structure identified in §3.2.1 and the vortex stretching and strain self-amplification mechanisms.…”

Section: Connection Between Conditional Flow Fields Vortex Stretchinmentioning

confidence: 99%

“…The previous works pertain to the energy transfer across flow scales under the influence of the mean shear, which is the most relevant case from the engineering and geophysical viewpoints. Still, it is worth mentioning that the inertial energy cascade has been classically ascribed to the stretching exerted among vortices at different scales in isotropic turbulence (Goto et al 2017;Motoori & Goto 2019), although recent works have debated this view in favour of strain-rate self-amplification as the main contributor to the energy transfer among scales (Carbone & Bragg 2019). The reader is referred to Alexakis & Biferale (2018) for an unified and exhaustive review of the different energy transfer mechanisms.…”

Section: Introductionmentioning

confidence: 99%

The coherent structure of the kinetic energy transfer in shear turbulence

et al. 2020

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The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex shaped as an inverted hairpin followed by an upright hairpin. The asymmetry between the forward and backward cascade arises from the opposite flow circulation within the hairpins, which triggers reversed patterns in the flow.

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Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers

Cited by 68 publications

References 56 publications

Time-Periodic Inertial Range Dynamics

Time-Periodic Inertial Range Dynamics

Turbulence generation through an iterative cascade of the elliptical instability

The coherent structure of the kinetic energy transfer in shear turbulence

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