Universality in fully developed turbulence

Siegfried Grossmann, Detlef Lohse

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We extend the numerical simulations of She et al. [Phys. Rev. Lett. 70, 3251 (1993)] of highly turbulent flow with 15 <= Taylor-Reynolds numbers Re lambda <= 200 up to Re lambda [approx equals] 45 000, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers Re lambda , the energy spectra as well as the higher moments - when scaled by the spectral intensity at the wave number kp of peak dissipation - can be described by one universal function of k/kp for all Re lambda . Second, the k-space inertial subrange scaling exponents zeta m of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the larger Re lambda is), as is the Re lambda dependence of kp. Only around kp, viscous damping leads to a slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).
Original languageUndefined
Pages (from-to)2784-2789
JournalPhysical review E: Statistical physics, plasmas, fluids, and related interdisciplinary topics
Issue number4
Publication statusPublished - 1994


  • IR-50334

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