When the back pressure ratio is large enough, the flow within the entire device will be subsonic and isentropic. When the back pressure ratio reaches a critical value, the flow will become choked with subsonic flow in the converging section, sonic flow at the throat, and subsonic flow in the diverging section.
A further decrease in the back pressure ratio results in the formation of a shock wave (shown as a red line) within the diverging section. The flow coming into the shock wave will be supersonic. Across the shock wave the flow properties change suddenly with the pressure, temperature, and density all increasing across the shock. The Mach number downstream of the shock wave will be subsonic. The location of the shock is such that the pressure at the diverging section exit will equal the back pressure. The flow upstream and downstream of the shock wave may be considered isentropic but the flow across the shock wave is non-isentropic.
As the back pressure ratio is decreased further, the shock wave moves downstream of the throat toward the exit of the device. Note that the "strength" of the shock wave, defined as the pressure ratio across the shock, increases as the shock moves away from the throat. Eventually, a critical back pressure is reached where the shock wave is located at the exit of the diverging section.
A further decrease results in the shock wave moving out of the nozzle to form oblique shock waves (represented as slanted, red lines in the schematic). The flow within the converging-diverging nozzle is isentropic since there are no shock waves within the device. Oblique shock waves appear outside the nozzle because the flow static pressure at the exit is lower than the back pressure and so the flow must be compressed to eventually reach the back pressure. This type of flow is referred to as over-expanded flow since the nozzle exit area is too large resulting in an exit pressure that is lower than the back pressure.
Over-expanded flow continues as the back pressure ratio is decreased until a critical back pressure ratio is reached where the exit pressure is exactly equal to the back pressure. This type of flow is called perfectly-expanded flow or flow at design conditions.
Dropping the back pressure ratio further results in a condition known as under-expanded flow. For this condition, the pressure at the exit is larger than the back pressure so the flow must continue to expand upon leaving the device. This occurs through a set of expansion fans at the exit (shown as green lines in the schematic). Dropping the back pressure further maintains under-expanded flow.