  A stochastic EDQNM approach is used to investigate self-similar decaying
isotropic turbulence at high Reynolds number ($400 \leq Re_\lambda \leq 10^4$).
The realistic energy spectrum functional form recently proposed by Meyers &
Meneveau is generalised by considering some of the model constants as random
parameters, since they escape measure in most experimental set-ups. The induced
uncertainty on the solution is investigated building response surfaces for
decay power-law exponents of usual physical quantities. Large-scale
uncertainties are considered, the emphasis being put on Saffman and Batchelor
turbulence. The sensitivity of the solution to initial spectrum uncertainties
is quantified through probability density functions of the decay exponents. It
is observed that initial spectrum shape at very large scales governs the
long-time evolution, even at high Reynolds number, a parameter which is not
explicitly taken into account in many theoretical works. Therefore, a universal
asymptotic behavior in which kinetic energy decays as $t^{-1}$ is not detected.
But this decay law is observed at finite Reynolds number with low probability
for some initial conditions.
