A simple spectral model is used to examine what is required to determine the energy
and integral scale in homogeneous isotropic turbulence. The problem is that these
are determined in part by the largest scales of the turbulence which are either not
simulated at all by DNS or experiments, or cannot be estimated because of an
insufficient statistical sample. The absence of scales an order of magnitude below
the peak in the energy spectrum is shown to affect the determination significantly.
Since this energy peak shifts to lower wavenumbers as the flow evolves, the problem
becomes progressively worse during decay. It is suggested that almost all reported
integral scales for isotropic decaying turbulence are questionable, and that the power
laws fitted to them are seriously in error. Approximate correction using the spectral
model shows that recent DNS data which decay as u2 ∝ tn
with constant n, are also consistent with L ∝ t1/2.