In this paper, Navier-Stokes equations were solved with high order accurate schemes to investigate the basic structure and regularity of the flow field during the interaction of a supersonic jet and a codirectional supersonic incoming flow. A double backward-facing step model was proposed to investigate the interaction between the jet/supersonic incoming flow shear layers. The two shear layers interact to produce a secondary jet. The secondary jet produced by the action has a unique periodicity that is related to the overall oscillation of the shear layer. The secondary jet is generated when the horizontal angle of the jet shear layer reaches a certain value. This paper focused on the analysis and discussion of the periodicity of the secondary jet. When the aspect ratio is different, the period of the secondary jet changes significantly. However, when the static pressure ratio is different, the period of the secondary jet does not change much. Published under license by AIP Publishing.