  A direct numerical simulation of an oblique shock wave impinging on a
turbulent boundary layer at Mach number 2.28 is carried out at moderate
Reynolds number, simulating flow conditions similar to those of the experiment
by Dupont et al. (2006). The low-frequency shock unsteadiness, whose
characteristics have been the focus of considerable research efforts, is here
investigated via the Morlet wavelet transform. Owing to its compact support in
both physical and Fourier spaces, the wavelet transformation makes it possible
to track the time evolution of the various scales of the wall-pressure
fluctuations. This property also makes it possible to define a local
intermittency measure, representing a frequency-dependent flatness factor, to
pinpoint the bursts of energy that characterise the shock intermittency scale
by scale. As a major result, wavelet decomposition shows that the broadband
shock movement is actually the result of a collection of sparse events in time,
each characterised by its own temporal scale. This feature is hidden by the
classical Fourier analysis, which can only show the time-averaged behaviour.
Then, we propose a procedure to process any relevant time series, such as the
time history of the wall-pressure or that of the separation bubble extent, in
which we use a condition based on the local intermittency measure to filter out
the turbulent content in the proximity of the shock foot and to isolate only
the intermittent component of the signal. In addition, wavelet analysis reveals
the intermittent behaviour also of the breathing motion of the recirculation
bubble behind the reflected shock, and allows us to detect a direct, partial
correspondence between the most significant intermittent events of the
separation region and those of the wall-pressure at the foot of the shock.
