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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