Energy transfer and dissipation in forced isotropic turbulence

Abstract

A model for the Reynolds number dependence of the dimensionless dissipation rate $C_{\epsilon }$ was derived from the dimensionless Kármán-Howarth equation, resulting in $C_{\epsilon }=C_{\epsilon ,\infty }+C/R_L+O(1/R_L^2)$, where $R_L$ is the integral scale Reynolds number. The coefficients $C$ and $C_{\epsilon ,\infty }$ 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 $R_L=5875$ ($R_{\lambda }=435$), 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 $n=-1.000\pm 0.009$, and that this decay of $C_{\epsilon }$ 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 $C=18.9\pm 1.3$ and in an asymptotic value for $C_{\epsilon }$ in the infinite Reynolds number limit of $C_{\epsilon ,\infty }=0.468\pm 0.006$.

26 pages including references and 6 figures. arXiv admin note: text overlap with arXiv:1307.4574

References in corpus (3)

• Spectral imbalance and the normalized dissipation rate of turbulence
• The "zeroth law" of turbulence: Isotropic turbulence simulations revisited
• Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

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