The supersonic jet interaction flow field generated by a sonic circular jet with a pressure ratio of 532 exhausting into a turbulent MACH 4.0 cross flow over a flat plate was investigated using numerical simulations. The simulations made use of the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations coupled with Wilcox's 1998 k-omega turbulence model. The numerical solution was validated with experimental data that include the pressure distribution on the flat plate, with an empirical formula for the height of the barrel shock, and with the Schlieren pictures showing the location and shape of the main shock formations. The simulations correctly captured the location and shape of the main flow features and compared favorably with the experimental pressure distribution on the flat plate. The validated numerical simulation was used to investigate in detail the flow physics. The flow field was found to be dominated by the shock formations and their coupling with the strong vortical structures. Three primary shock formations were observed: a barrel shock, a bow shock, and a separation-induced shock wave. While the general structure of the barrel shock was found to be similar to that of the underexpanded jet exhausting into a quiescent medium, two unique features distinguished the flow field: the concave indentation in the leeside of the recompression (barrel) shock and the folding of the windward side of the barrel shock due to an inner reflection line. The presence of the steep pressure gradients associated with the shocks creates strong vortical motions in the fluid. Six primary vortices were identified: (i) the well-known horseshoe vortex, (ii) an upper trailing vortex, (iii) two trailing vortices formed in the separation region and, aft of the bow shock wave, (iv) two more trailing vortices that eventually merge together into one single rotational motion. The low-pressure region aft of the injector was found to be generated by the combined effect of the concave indentation in the leeside of the barrel shock and the lower trailing vortices. The trailing vortices were found to be the main mechanism responsible for the mixing of the injectant with the freestream fluid.