Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

Motoori, Yutaro; Goto, Susumu

doi:10.1017/jfm.2019.76

Cited by 57 publications

(88 citation statements)

References 52 publications

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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].…”

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confidence: 90%

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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confidence: 90%

Turbulence generation through an iterative cascade of the elliptical instability

et al. 2020

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“…If g is positively large, the vortices at σ ω are stretched by strain rates at σ S , whereas they are compressed when g is negatively large. As was demonstrated in our previous study (Motoori and Goto, 2019), the generation mechanism of vortices depends on the distance from the wall and the scale of vortices. In the log layer, while vortices lager than approximately one-fifth of the height are stretched and amplified directly by the mean flow, smaller (narrower band-pass filter) in Fig.…”

Section: Enstrophy Production Ratessupporting

confidence: 60%

“…We numerically investigate a turbulent boundary layer with zero pressure gradient over a flat plate, which is the same field previously reported by Motoori and Goto (2019). The Navier-Stokes equations for an incompressible fluid are integrated using the simplified marker and cell (SMAC) method (Amsden and Harlow, 1970).…”

Section: Direct Numerical Simulationmentioning

confidence: 98%

“…For example, many authors (Lee and Sung, 2011;Lee et al, 2014;Hwang et al, 2016;Lee et al, 2017) used the filter to highlight the large-scale motions, and Lozano-Durán et al (2016) analyzed the dynamics of the filtered velocity gradient in the log layer in turbulent channel flow. We also used the Gaussian filter to reveal the scale-dependent contribution to the enstrophy production rates in a turbulent boundary layer (Motoori and Goto, 2019). However, we must note that the Gaussian-filtered turbulent velocity fields, which correspond to the low-pass filtered fields, possess the information of all scales larger than the filter scale.…”

Section: Introductionmentioning

confidence: 99%

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Scale-dependent enstrophy production rates in a turbulent boundary layer

Motoori

Goto

2019

JFST

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Coarse-graining is indispensable for extracting a hierarchy of vortices in fully developed turbulent flow with multiscale nature. In the present study, for a high-Reynolds-number turbulent boundary layer, we employ two simple coarse-graining methods in real space; namely, a Gaussian filter and the combination of the Gaussian filters at two scales. The former corresponds to a low-pass filter of Fourier modes, while the latter corresponds to a band-pass filter. We also examine two different filter widths for the band-pass filter. Then, we show difference in the statistics of the three filtered fields. Since the velocity gradients in turbulence are mainly determined by the smallest-scale motions, vortical structures identified by the second invariant Q of the velocity gradient coarse-grained by the filters are similar. However, there is difference between low-and band-pass filtered fields in the contribution to the enstrophy production rates. This is because the production rates are determined not only by the magnitude of the strain rates but also by the alignment between the vorticity and the stretching direction. In addition, since vortices are not created in the entire system, the conditional sampling by the value of Q is essential to understand the generation mechanism of the hierarchy of vortices. The conditional analysis of the band-pass filtered fields demonstrates that small-scale vortices in the log layer are stretched by twice-larger vortices, whereas they weaken the twice-larger vortices. This observation is consistent with the picture of the energy cascade. We also show that when using the band-pass filter, these conclusions are robust irrespective of the choice of the filter width.

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“…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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Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

Cited by 57 publications

References 52 publications

Turbulence generation through an iterative cascade of the elliptical instability

Turbulence generation through an iterative cascade of the elliptical instability

Scale-dependent enstrophy production rates in a turbulent boundary layer

The coherent structure of the kinetic energy transfer in shear turbulence

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