Energy transfer and dissipation in forced isotropic turbulence

A model for the Reynolds-number dependence of the dimensionless dissipation rate C_ was derived from the dimensionless K\'arm\'an-Howarth equation, resulting in C_=C, +C/R₋+O (1/R₋^2), where R₋ is the integral scale Reynolds number. The coefficients C and C, 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₋=5875 (R_=435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R₋^n with exponent value n=-1. 0000. 009 and that this decay of C_ was actually due to the increase in the Taylor surrogate U^3/L. The model equation was fitted to data from the DNS, which resulted in the value C=18. 91. 3 and in an asymptotic value for C_ in the infinite Reynolds-number limit of C, =0. 4680. 006.