Answer by Thomas Zerbarini:
The double wall at the after nozzle is to reduce noise and exhaust temperature.
The noise reduction is to be more noise friendly. The reduction in exhaust temperature is to reduce the heat signature to reduce the aircrafts ability to be tracked and locked onto by heat seeking radar missiles.
To achieve a lower noise and heat signature the outer portion of the jet engine is for cool bypass air to shroud and mix with the hot exhaust air…