Spectral imbalance and the normalized dissipation rate of turbulence

The normalized turbulent dissipation rate Cϵ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of Cϵ 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 Cϵ 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 Cϵ at low Reynolds number that is observed in the simulations.