  We study structure formation using relativistic cosmological linear
perturbation theory in the presence of intrinsic and relative (with respect to
matter) non-adiabatic dark energy perturbations. For different dark energy
models we assess the impact of non-adiabaticity on the matter growth promoting
a comparison with growth rate data. The dark energy models studied lead to
peculiar signatures of the (non)adiabatic nature of dark energy perturbations
in the evolution of the $f \sigma_{8}(z)$ observable. We show that
non-adiabatic DE models become close to be degenerated with respect to the
$\Lambda$CDM model at first order in linear perturbations. This would avoid the
identification of the non-adiabatic nature of dark energy using current
available data. Therefore, such evidence indicates that new probes are
necessary to reveal the non-adiabatic features in the dark energy sector.
