  For Burgers equations with real data and complex forcing terms, Lerner,
Morimoto and Xu [{\it Instability of the Cauchy-Kovalevskaya solution for a
class of non-linear systems}, Amer.~J.~Math.~2010] proved that only analytical
data generate local $C^2$ solutions. The corresponding instabilities are
however not observed numerically; rather, numerical simulations show an
exponential growth only after a delay in time. We argue that numerical
diffusion is responsible for this time delay, as we prove that for Burgers
equations in the torus with small viscosity and a complex forcing, oscillating
data generate solutions which grow linearly in time before growing
exponentially. Numerical simulations illustrate the results.
