TY - JOUR

T1 - Statistics of local Reynolds number in box turbulence

T2 - Ratio of inertial to viscous forces

AU - Kaneda, Yukio

AU - Ishihara, Takashi

AU - Morishita, Koji

AU - Yokokawa, Mitsuo

AU - Uno, Atsuya

N1 - Funding Information:
This study was partly supported by JSPS KAKENHI, grant numbers JP16H06339, JP19H00641 and 20H01948. The computational resources of the K computer and the supercomputer Fugaku provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project (Projects ID: hp180109, ID: hp190076, ID: hp200184 and ID: hp210138) were partly used in this study. This study was also partly supported by ‘Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures’ (Projects ID: jh190068, ID: jh200021 and ID: jh210034).
Publisher Copyright:
© 2021 The Author(s).

PY - 2021/12/25

Y1 - 2021/12/25

N2 - In high-Reynolds-number turbulence the spatial distribution of velocity fluctuation at small scales is strongly non-uniform. In accordance with the non-uniformity, the distributions of the inertial and viscous forces are also non-uniform. According to direct numerical simulation (DNS) of forced turbulence of an incompressible fluid obeying the Navier-Stokes equation in a periodic box at the Taylor microscale Reynolds number Rλ ≈ 1100, the average 〈Rloc〉 over the space of the 'local Reynolds number' Rloc, which is defined as the ratio of inertial to viscous forces at each point in the flow, is much smaller than the conventional 'Reynolds number' given by Re ≡ UL/ν, where U and L are the characteristic velocity and length of the energy-containing eddies, and ν is the kinematic viscosity. While both conditional averages of the inertial and viscous forces for a given squared vorticity ω2 increase with ω2 at large ω2, the conditional average of Rloc is almost independent of ω2. A comparison of the DNS field with a random structureless velocity field suggests that the increase in the conditional average of Rloc with ω2 at large ω2 is suppressed by the Navier-Stokes dynamics. Something similar is also true for the conditional averages for a given local energy dissipation rate per unit mass. Certain features of intermittency effects such as that on the Re dependence of 〈Rloc〉 are explained by a multi-fractal model by Dubrulle (J. Fluid Mech., vol. 867, 2019, P1).

AB - In high-Reynolds-number turbulence the spatial distribution of velocity fluctuation at small scales is strongly non-uniform. In accordance with the non-uniformity, the distributions of the inertial and viscous forces are also non-uniform. According to direct numerical simulation (DNS) of forced turbulence of an incompressible fluid obeying the Navier-Stokes equation in a periodic box at the Taylor microscale Reynolds number Rλ ≈ 1100, the average 〈Rloc〉 over the space of the 'local Reynolds number' Rloc, which is defined as the ratio of inertial to viscous forces at each point in the flow, is much smaller than the conventional 'Reynolds number' given by Re ≡ UL/ν, where U and L are the characteristic velocity and length of the energy-containing eddies, and ν is the kinematic viscosity. While both conditional averages of the inertial and viscous forces for a given squared vorticity ω2 increase with ω2 at large ω2, the conditional average of Rloc is almost independent of ω2. A comparison of the DNS field with a random structureless velocity field suggests that the increase in the conditional average of Rloc with ω2 at large ω2 is suppressed by the Navier-Stokes dynamics. Something similar is also true for the conditional averages for a given local energy dissipation rate per unit mass. Certain features of intermittency effects such as that on the Re dependence of 〈Rloc〉 are explained by a multi-fractal model by Dubrulle (J. Fluid Mech., vol. 867, 2019, P1).

KW - general fluid mechanics

KW - homogeneous turbulence

KW - isotropic turbulence

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U2 - 10.1017/jfm.2021.806

DO - 10.1017/jfm.2021.806

M3 - Article

AN - SCOPUS:85118373620

VL - 929

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - A1

ER -