Jogging my old memory, Back in '69 aboard U.S.S. Saratoga on a Mediterranean Cruise, it was target practice time for 
the A-7s from VA-75.  The ship was towing a target about 500 yards behind and the A-7s were swooping down from a 
higher altitude to take their shots.  Many of them were cracking the sound barrier after firing and pulling up.

3 hours ago, Christopher Low said:

What happens if an aircraft travelling at a ground speed of over 800 mph (due to being pushed by a very fast jetstream) suddenly drops out of that regime into normal atmospheric conditions? Is that possible, or are the edges of the jetstream very well defined and stable (so that this can be avoided)?

The effect is similar to going through a patch of clear air turbulence.  The groundspeed will obviously change significantly and be reflected in the aircraft navigation systems. The airspeed will typically flutter a little bit, as it often does in CAT from other causes. This is not usually significant or long lasting. It's often the result of temperature differences in the two air masses. The change in groundspeed in itself has no aerodynamic effect on the aircraft, but indirect effects due to the other factors causing the change in grounspeed may be noticed.