Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation

Ishihara, Takashi; Gotoh, Toshiyuki; Kaneda, Yukio

doi:10.1146/annurev.fluid.010908.165203

Cited by 597 publications

(520 citation statements)

References 75 publications

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“…3, the second and third panels of which show successively magnified images of the central part of the first panel (for a 4096 3 version see Ref. [79]). One method to look at these structures is to study the joint PDF of the invariants Q = −tr(A 2 )/2 and R = −tr(A 3 )/3 of the velocity gradient tensor.…”

Section: D Navier-stokes Turbulencementioning

confidence: 99%

Statistical properties of turbulence: An overview

2009

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Section: D Navier-stokes Turbulencementioning

confidence: 99%

Statistical properties of turbulence: An overview

2009

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“…It is widely acknowledged (but not universally acceptedsee Davidson 2004, p.77) that A 1 is a universal constant at asymptotically large Reynolds numbers. While the simulations of isotropic turbulence by Ishihara et al (2009) show that A 1 asymptotes to a constant as the Taylor microscale Reynolds number, Re λ → 1200, they also show finite Reynolds number effects. The work of Vassilicos (2015) and colleagues has considered the nonequilibrium effects of initial and large-scale conditions.…”

Section: Introductionmentioning

confidence: 97%

“…Even so, Kolmogorov (1962, here designated as K62) himself had to refine his theory of "universal equilibrium" (see also Obukhov 1962) in order to account for departures from local isotropy due to the effects of spatial fluctuations of the energy dissipation rate. While these papers are admirably concise in themselves, it is hardly surprising that they continue to be the subject of much interest: excellent summaries with historical perspectives are provided by Kraichnan (1974); Sreenivasan (1991); Sreenivasan & Antonia (1997), Ishihara et al (2009) and Vassilicos (2015).…”

Section: Introductionmentioning

confidence: 99%

“…Yet, little is known about the origins of intermittency and whether it might be attributable to the effects of Reynolds number, mean shear or solid boundaries, or whether it is intrinsic to the Navier-Stokes equations themselves (Kraichnan 1974). Ishihara et al (2009) illustrate the importance of internal shear layers that lead to intermittency. Nor is it straightforward to separate out the effects of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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The inertial subrange in turbulent pipe flow: centreline

2016

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The inertial subrange scaling of the axial velocity component is examined for the centre line of turbulent pipe flow for Reynolds numbers in the range 249 Re λ 986. Estimates of the dissipation rate are made by both integration of the one-dimensional dissipation spectrum and the third-order moment of the structure function. In neither case does the non-dimensional dissipation rate asymptote to a constant; rather than decreasing, it increases indefinitely with Reynolds number. Complete similarity of the inertial range spectra is not evident: there is little support for K41, and effects of Reynolds number are not well represented by Kolmogorov's "extended similarity hypothesis", K62. The second-order moment of the structure function does not show a constant value, even when compensated by K62. When corrected for the effects of finite Reynolds number, the third-order moments of the structure function accurately support the " 4 5 ths" law, but they do not show a clear plateau. In common with recent work in grid turbulence, nonequilibrium effects can be represented by an heuristic scaling that includes a global Reynolds number as well as a local one. It is likely that nonequilibrium effects appear to be particular to the nature of the boundary conditions. Here, the principal effects of the boundary conditions appear through finite turbulent transport at the pipe centre line which constitutes a source or a sink at each wavenumber.

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“…The basic result of (1.1) is that, at sufficiently large Reynolds numbers, an intermediate range of scales exists, away from energy injection and energy dissipation, where the energy flux across scales is identified as δu 3 /r. This expression provides a direct evaluation of the energy cascade through the inertial range (see Nie & Tanveer 1999;Aoyama et al 2005;Gotoh & Watanabe 2005;Ishihara, Gotoh & Kaneda 2009). …”

Section: Introductionmentioning

confidence: 99%

Cascades and wall-normal fluxes in turbulent channel flows

et al. 2016

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The present work describes the multidimensional behaviour of scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the near-wall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wall-bounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scale-energy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role.

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Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation

Cited by 597 publications

References 75 publications

Statistical properties of turbulence: An overview

Statistical properties of turbulence: An overview

The inertial subrange in turbulent pipe flow: centreline

Cascades and wall-normal fluxes in turbulent channel flows

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