Dissipation range of the energy spectrum in high Reynolds number turbulence

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 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.