We study the two-dimensional turbulent transonic flow past a symmetric profile with a blunt base and flat sides. The numerical simulation is based on the unsteady Reynolds-averaged Navier-Stokes equations. The obtained solutions reveal both symmetric and asymmetric oscillating flows past the profile at zero angle of attack. An occurrence of the symmetric or asymmetric flow regime depends on the time history of boundary conditions. A jet injection into the wake does not eliminate the flow non-uniqueness, though attenuates flow oscillations.