A model for the Reynolds number dependence of the dimensionless dissipation rate Cε was derived from the dimensionless Kármán-Howarth equation, resulting in Cε = Cε,∞ +C/RL + O(1/RL ), where RL is the integral scale Reynolds number. The coefficients C and Cε,∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law RLn with exponent value n = −1.000 ± 0.009, and that this decay of Cε was actually due to the increase in the Taylor surrogate U3/L. The model equation was fitted to data from the DNS which resulted in the value C = 18.9 ± 1.3 and in an asymptotic value for Cε in the infinite Reynolds number limit of Cε,∞ = 0.468 ± 0.006.
- energy transfer
- isotropic turbulence
- direct numerical simulation
McComb, W. D., Berera, A., Yoffe, S. R., & Linkmann, M. F. (2015). Energy transfer and dissipation in forced isotropic turbulence. Physical Review E, 91(4), . https://doi.org/10.1103/PhysRevE.91.043013