Energy Spectrum in the Near Dissipation Range of High Resolution Direct Numerical Simulation of Turbulence

The energy spectrum in the near dissipation range of turbulence is studied by analyzing the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence in a periodic box with the Taylor micro-scale Reynolds number R λ and resolution ranging up to about 675 and 4096 3 , respectively. The spectra in the Reynolds number range fit well to the form C ( k η) α exp (-β k η) in the wavenumber range \(0.5 \lesssim k\eta \lesssim 1.5\), where η is the Kolmogorov dissipation length scale and C , α and β are constants independent of k . The values of α and β decrease monotonically with R λ , and they are consistent with the conjecture that they approach to constants as R λ →∞, but the approach, especially that of β, is slow.