TY - JOUR
T1 - Dissipation range of the energy spectrum in high Reynolds number turbulence
AU - Buaria, Dhawal
AU - Sreenivasan, Katepalli R.
N1 - Publisher Copyright:
© 2020 authors.
PY - 2020/9
Y1 - 2020/9
N2 - We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to Rλ=650, with excellent small-scale resolution of kmaxη≈6, and additionally at Rλ=1300 with kmaxη≈3, where kmax is the maximum resolved wave number and η is the Kolmogorov length scale. We find that for a limited range of wave numbers k past the bottleneck, in the range 0.15kη0.5, the spectra for all Rλ display a universal stretched exponential behavior of the form exp(-k2/3), in rough accordance with recent theoretical predictions. In contrast, the stretched exponential fit does not possess a unique exponent in the near dissipation range 1kη4, but one that persistently decreases with increasing Rλ. This region serves as the intermediate dissipation range between the exp(-k2/3) region and the far dissipation range kη≫1 where analytical arguments as well as DNS data with superfine resolution [S. Khurshid, Phys. Rev. Fluids 3, 082601 (2018)10.1103/PhysRevFluids.3.082601] suggest a simple exp(-kη) dependence. We briefly discuss our results in connection to the multifractal model.
AB - We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to Rλ=650, with excellent small-scale resolution of kmaxη≈6, and additionally at Rλ=1300 with kmaxη≈3, where kmax is the maximum resolved wave number and η is the Kolmogorov length scale. We find that for a limited range of wave numbers k past the bottleneck, in the range 0.15kη0.5, the spectra for all Rλ display a universal stretched exponential behavior of the form exp(-k2/3), in rough accordance with recent theoretical predictions. In contrast, the stretched exponential fit does not possess a unique exponent in the near dissipation range 1kη4, but one that persistently decreases with increasing Rλ. This region serves as the intermediate dissipation range between the exp(-k2/3) region and the far dissipation range kη≫1 where analytical arguments as well as DNS data with superfine resolution [S. Khurshid, Phys. Rev. Fluids 3, 082601 (2018)10.1103/PhysRevFluids.3.082601] suggest a simple exp(-kη) dependence. We briefly discuss our results in connection to the multifractal model.
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U2 - 10.1103/PhysRevFluids.5.092601
DO - 10.1103/PhysRevFluids.5.092601
M3 - Article
AN - SCOPUS:85092460179
SN - 2469-990X
VL - 5
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 9
M1 - 092601
ER -