  We present a numerical study of an idealized magnetohydrodynamic (MHD)
configuration consisting of a planar wake flow embedded into a
three-dimensional (3D) sheared magnetic field. Our simulations investigate the
possibility for in-situ development of large-scale compressive disturbances at
cospatial current sheet -- velocity shear regions in the heliosphere. Using a
linear MHD solver, we first systematically chart the destabilized wavenumbers,
corresponding growth rates, and physical parameter ranges for dominant 3D
sinuous-type instabilities in an equilibrium wake--current sheet system. Wakes
bounded by sufficiently supersonic (Mach number $M_s > 2.6$) flow streams are
found to support dominant fully 3D sinuous instabilities when the plasma beta
is of order unity. Fully nonlinear, compressible 2.5D and 3D MHD simulations
show the self-consistent formation of shock fronts of fast magnetosonic type.
They carry density perturbations far away from the wake's center. Shock
formation conditions are identified in sonic and Alfv\'enic Mach number
parameter space. Depending on the wake velocity contrast and magnetic field
magnitude, as well as on the initial perturbation, the emerging shock patterns
can be plane-parallel as well as fully three-dimensionally structured. Similar
large-scale transients could therefore originate at distances far above coronal
helmet streamers or at the location of the ecliptic current sheet.
