  The complex interaction between shocks and plasma turbulence is extremely
important to address crucial features of energy conversion in a broad range of
astrophysical systems. We study the interaction between a supercritical,
perpendicular shock and pre-existing, fully-developed plasma turbulence,
employing a novel combination of magnetohydrodynamic (MHD) and small-scale,
hybrid-kinetic simulations where a shock is propagating through a turbulent
medium. The variability of the shock front in the unperturbed case and for two
levels of upstream fluctuations is addressed.We find that the behaviour of
shock ripples, i.e., shock surface fluctuations with short (a few ion skin
depths, $d_i$) wavelengths, is modified by the presence of pre-existing
turbulence, which also induces strong corrugations of the shock front at larger
scales. We link this complex behaviour of the shock front and the shock
downstream structuring with the proton temperature anisotropies produced in the
shock-turbulence system. Finally, we put our modelling effort in the context of
spacecraft observations, elucidating the role of novel cross-scale,
multi-spacecraft measurements in resolving shock front irregularities at
different scales. These results are relevant for a broad range of astrophysical
systems characterised by the presence of shock waves interacting with plasma
turbulence.
