Energy transfer and dissipation in forced isotropic turbulence.

Abstract

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(L)(2)), 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(L)(n) 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 U(3)/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.