Energy transfer and dissipation in forced isotropic turbulence

A model for the Reynolds number dependence of the dimensionless dissipation rate C_ɛ is derived from the dimensionless Kármán-Howarth equation, resulting in C_ɛ =C_{ɛ , ∞} + C /R_L , where R_L is the integral scale Reynolds number. The coefficients C and C_{ɛ , ∞} arise from asymptotic expansions of the dimensionless second- and third-order structure functions. The model equation is fitted to data from direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to R_L = 5875 (R_λ = 435), which results in an asymptote for C_ɛ in the infinite Reynolds number limit C_{ɛ , ∞} = 0 . 47 +/- 0 . 01 . Since the coefficients in the model equation are scale-dependent while the dimensionless dissipation rate is not, we modelled the scale dependences of the coefficients by an ad hoc profile function such that they cancel out, leaving the model equation scale-independent, as it must be. The profile function was compared to DNS data to very good agreement, provided we restrict the comparison to scales small enough to be well resolved in our simulations.

This work has made use of the resources provided by the UK supercomputing service HECToR, made available through the Edinburgh Compute and Data Facility (ECDF). A.B. is supported by STFC, S.R.Y. and M.F.L. are funded by EPSRC.