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.
ASJC Scopus subject areas
- Computational Mechanics
- Modeling and Simulation
- Fluid Flow and Transfer Processes