Abstract
Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 8192^{3} periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.
Highlights
This Rapid Communication resolves the previously contradictory results on inertial-range universality, to be described immediately below, of two orthogonal velocity increments in isotropic turbulence
The power-law scaling of both the longitudinal and transverse structure functions with respect to r should be the same for inertial-range universality to hold, where the inertial range is the range of separation distances r which are small compared to the large scale of turbulence but large compared to the viscous cut-off scale
We have used direct numerical simulation (DNS) data at high Reynolds numbers to assess the past assertion that the longitudinal and transverse velocity structure functions scale differently in the inertial range. This difference was thought to be connected to the notion that the longitudinal velocity increments are connected to dissipation and the transverse velocity increments are connected to enstrophy, while the dissipation and enstrophy themselves have different probability density functions (PDFs)
Summary
Iyer* Department of Physics and INFN, University of Rome Tor Vergata, Rome 00133, Italy and Department of Mechanical Engineering, New York University, New York 11201, USA. Sreenivasan Departments of Physics and Mechanical Engineering and the Courant Institute of Mathematical Sciences, New York University, New York 11201, USA. Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 81923 periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov’s refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range
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