  Context. Theoretical arguments and numerical simulations of radiative shocks
produced by the impact of the accreting gas onto young stars predict
quasi-periodic oscillations in the emitted radiation. However, observational
data do not show evidence of such periodicity. Aims. We investigate whether
physically plausible perturbations in the accretion column or in the
chromosphere could disrupt the shock structure influencing the observability of
the oscillatory behavior. Methods. We performed local 2D magneto-hydrodynamical
simulations of an accretion shock impacting a chromosphere, taking optically
thin radiation losses and thermal conduction into account. We investigated the
effects of several perturbation types, such as clumps in the accretion stream
or chromospheric fluctuations, and also explored a wide range of plasma-\beta
values. Results. In the case of a weak magnetic field, the post-shock region
shows chaotic motion and mixing, smoothing out the perturbations and retaining
a global periodic signature. On the other hand, a strong magnetic field
confines the plasma in flux tubes, which leads to the formation of fibrils that
oscillate independently. Realistic values for the amplitude, length, and time
scales of the perturbation are capable of bringing the fibril oscillations out
of phase, suppressing the periodicity of the emission. Conclusions. The
strength of a locally uniform magnetic field in YSO accretion shocks determines
the structure of the post-shock region, namely, whether it will be somewhat
homogeneous or if it will split up to form a collection of fibrils. In the
second case, the size and shape of the fibrils is found to depend strongly on
the plasma-\beta value but not on the perturbation type. Therefore, the actual
value of the protostellar magnetic field is expected to play a critical role in
the time dependence of the observable emission.
