Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations
Résumé
We present a statistical analysis of the behavior of the kinetic energy spectrum in the dissipative range of fully developed three-dimensional turbulence, with the aim of testing a recent prediction obtained from the non-perturbative renormalization group. Analyzing spectra recorded in experiments of grid turbulence, generated in the Modane wind tunnel, and spectra obtained from high-resolution direct numerical simulations of the forced Navier-Stokes equation, we observe that the spectra decay as a stretched exponential in the dissipative range. The theory predicts a stretching exponent α = 2/3, and the data analyses of the numerical and experimental spectra are in close agreement with this value. This result also corroborates previous DNS studies which found that the spectrum in the near-dissipative range is best modeled by a stretched exponential with α < 1.
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