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As explained in this answer, the shocks in supersonic jet exhaust are created from the ambient air pressure compressing the exhaust stream. This eventually makes a shockwave, which reflects and then travels outwards to the boundary of the jet exhaust. My question is why doesn’t the shock just keep traveling outward instead stopping at the boundary to the atmospheric air as it does in the picture? (Look to the right of the red discs)

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Notice where it says the nozzle is overexpanded -- Pe < Pa. That means that at the Nozzle Exit, the pressure is less than ambient.

After the nozzle, there is no rigid wall against the flow, so the boundary between the jet exhaust (white) and the ambient (blue) is a slip line, which means pressure must be equal.

As the notes say, this forces the initial shock -- it must jump the pressure, but as a consequence, it also turns the flow.

There are a series of interactions and reflections that then happen. It is often beneficial to think of the center line as a solid wall. Symmetry can often be treated like a solid inviscid wall.

The white flow is supersonic -- usually substantially so. The ambient flow is much slower. Possibly supersonic, but it could also be subsonic or static. When you see photos of shock diamonds from an engine test stand, it is obviously static.

The shock that emanates from the triple point and trails aft (from the red disk) is turning the flow back to parallel (notice the symmetry line nearby). When that shock hits the ambient, if it were to continue, the pressure would not be equal. Consequently, that shock reflects as an expansion fan, which turns the flow out.

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