Energy spectrum in high-resolution direct numerical simulations of turbulence
Access this Article
A study is made about the energy spectrum E(k) of turbulence on the basis of high-resolution direct numerical simulations (DNSs) of forced incompressible turbulence in a periodic box using a Fourier spectral method with the number of grid points and the Taylor scale Reynolds number Rλ up to 122883 and approximately 2300, respectively. The DNS data show that there is a wave-number range (approximately 5×10−3<kη<2×10−2) in which E(k) fits approximately well to Kolmogorov's k−5/3 scaling, where η is the Kolmogorov length scale. However, a close inspection shows that the exponent is a little smaller than −5/3, and E(k) in the range fits to E(k)/[⟨ε⟩2/3k−5/3]=c(kL)m, where ⟨ε⟩ is the mean energy dissipation rate per unit mass; L is the integral length scale; and m≈−0.12. The coefficient c is independent of k, but has a Rλ dependence, such as c=CRζλ, where C≈0.9 and ζ≈0.14.
- Physical Review Fluids
Physical Review Fluids (1), 082403R-082403R, 2016-12-22
American Physical Society