Oscillations and bifurcation of the 2D turbulent airflow over a flat-sided symmetric wedge with a blunt trailing edge/base are studied numerically. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate the existence of asymmetric flow regimes in a band of the free-stream Mach number at zero angle of attack. The realization of a certain regime depends on initial and boundary conditions. There is a hysteresis in the dependence of flow field on the angle of attack. An air injection into the wake attenuates flow oscillations, though does not eliminate the existence of asymmetric regimes.