  Resolvent analysis is used to study the low-frequency behaviour of the
laminar oblique shock wave / boundary layer interaction (SWBLI). It is shown
that the computed optimal gain, which can be seen as a transfer function of the
system, follows a first-order low-pass filter equation, recovering the results
of Touber and Sandham (JFM, 2011). This behaviour is understood as proceeding
from the excitation of a single stable, steady global mode whose damping rate
sets the time scale of the filter. Different Mach and Reynolds numbers are
studied, covering different recirculation lengths $L$. This damping rate is
found to scale as $1/L$, leading to a constant Strouhal number $St_L$ as
observed in the literature. It is associated with a breathing motion of the
recirculation bubble. This analysis furthermore supports the idea that the
low-frequency dynamics of the SWBLI is a forced dynamics, in which background
perturbations continuously excite the flow. The investigation is then carried
out for 3D perturbations for which two regimes are identified. At low wave
numbers of the order of $L$, a modal mechanism similar to that of 2D
perturbations is found and exhibits larger values of the optimal gain. At
larger wave numbers of the order of the boundary layer thickness, the growth of
streaks, which results from a non-modal mechanism, is detected. No interaction
with the recirculation region is observed. Based on these results, the
potential prevalence of 3D effects in the low-frequency dynamics of the SWBLI
is discussed.
