  Direct numerical simulation of the Navier-Stokes equations is carried out to
investigate the interaction of a conical shock wave with a turbulent boundary
layer developing over a flat plate at free-stream Mach number $M_\infty = 2.05$
and Reynolds number $Re_\theta \approx 630$, based on the upstream boundary
layer momentum thickness. The shock is generated by a circular cone with half
opening angle $\theta _c = 25^\circ$. As found in experiments, the wall
pressure exhibits a distinctive N-wave signature, with a sharp peak right past
the precursor shock generated at the cone apex, followed by an extended zone
with favourable pressure gradient, and terminated by the trailing shock
associated with recompression in the wake of the cone. The boundary layer
behavior is strongly affected by the imposed pressure gradient, with streaks
which are locally suppressed in adverse pressure gradient (APG) zones, and
which suddenly reform in the downstream region with favourable pressure
gradient (FPG). Three-dimensional mean flow separation is only observed in the
first APG region associated with formation of a horseshoe vortex, whereas the
second APG region features an incipient detachment state, with scattered spots
of instantaneous reversed flow. As found in canonical two-dimensional
wedge-generated shock/boundary layer interactions, different amplification of
the turbulent stress components is observed through the interacting shock
system, with approach to isotropic state in APG regions, and to a two-component
anisotropic state in FPG.
