  Context. Supernova remnants (SNR) are one of the main sources of galactic
cosmic rays acceleration. This acceleration, believed to happen at the blast
wave front, leads to an energy loss at the shock front. This results in the
apparent proximity between the blast wave and the contact discontinuity. Aims.
In this article, we study the effect that turbulent-like density perturbations
of the interstellar medium (ISM) have on the evolution of young SNRs. We focus
on the impact such fluctuations have on the SNRs structure and more precisely
on the resulting distance between blast wave and contact discontinuity. Since
cosmic rays acceleration is necessary to explain this distance, this study
indirectly put into question the cosmic rays acceleration at the blast wave
front. Methods. We performed a set of purely hydrodynamic three-dimensional
simulations without cosmic ray acceleration in a co-expanding frame. We
randomly initialised the density variation of the interstellar medium following
a Kolmogorov power law. The resulting ratios of radii between blast wave,
contact discontinuity and reverse shock are then compared to the astronomical
observations. Results. The addition of density perturbation doesnt
significantly change the average ratio of radii. However, the simulations show
a higher growth of interfacial instabilities in the presence of a turbulent
ISM. The resulting deformation of the contact discontinuity could explain the
proximity between contact discontinuity and blast wave. They also explain the
plateau in the radial distribution of the line of sight velocity associated
with the observations of Tycho. Conclusions. The density perturbation of the
ISM should not be neglected in the simulation of young SNR as they have an
impact comparable to the cosmic rays acceleration on the SNR structure.
