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Journal Articles Physics of Fluids Year : 2007

Spectral imbalance and the normalized dissipation rate of turbulence

Abstract

The normalized turbulent dissipation rate $C_\epsilon$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_\epsilon$ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of $C_\epsilon$ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of $C_\epsilon$ at low Reynolds number that is observed in the simulations.
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Dates and versions

hal-00198496 , version 1 (17-12-2007)

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Wouter J.T. Bos, L. Shao, Jean-Pierre Bertoglio. Spectral imbalance and the normalized dissipation rate of turbulence. Physics of Fluids, 2007, 19, pp.045101. ⟨10.1063/1.2714079⟩. ⟨hal-00198496⟩
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