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Abstract:
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 R-lambda = 650, with excellent small-scale resolution of k(max) eta approximate to 6, and additionally at R-lambda = 1300 with k(max) eta approximate to 3, where k(max) is the maximum resolved wave number and eta is the Kolmogorov length scale. We find that for a limited range of wave numbers k past the bottleneck, in the range 0.15 less than or similar to k eta <= 0.5, the spectra for all R-lambda display a universal stretched exponential behavior of the form exp(-k(2/3)), in rough accordance with recent theoretical predictions. In contrast, the stretched exponential fit does not possess a unique exponent in the near dissipation range 1 <= k eta <= 4, but one that persistently decreases with increasing R-lambda. This region serves as the intermediate dissipation range between the exp(-k(2/3)) region and the far dissipation range k eta >> 1 where analytical arguments as well as DNS data with superfine resolution [S. Khurshid et al., Phys. Rev. Fluids 3, 082601 (2018)] suggest a simple exp(-k eta) dependence. We briefly discuss our results in connection to the multifractal model.
