Energy transfer and dissipation in forced isotropic turbulence

A model for the Reynolds-number dependence of the dimensionless dissipation rate C_ɛ was derived from the dimensionless Kármán-Howarth equation, resulting in C_ɛ=C_{ɛ ,∞}+C /R_L+O (1 /R_L²) , 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. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to R_L=5875 (R_λ=435 ), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R_Lⁿ with exponent value n =-1.000 ±0.009 and that this decay of C_ɛ 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 C_ɛ in the infinite Reynolds-number limit of C_{ɛ ,∞}=0.468 ±0.006 .