After a lot of digging around, I found this.
...the main noise-reduction technique is to redesign the aircraft to
reshape the acoustic signature. A sonic boom consists of a double bang
on the ground that is caused by two large pressure pulses. As the
random shockwaves travel away from the aircraft at the speed of sound,
they pile up and coalesce. The engineers aim to reshape the acoustic
signature of the boom by preventing sonic waves piling up.
“You shape every aspect of the airplane to make the shockwaves as
close to equal strength as you can. When they’re as evenly distributed
as possible along the length of the airplane, changes in temperature
are small and the waves don’t coalesce. When the signal reaches the
ground, it’s smeared out. Instead of two loud bangs, there’s a
pressure change and a soft thump,” says Peter Coen, NASA’s commercial
supersonic technology project manager.
Source: Aerospace Testing International, Dec 2018: Supersonic testing: Boom or bust?
I realize this doesn't answer the question of the physics, but I thought i would stick within my paygrade. Someone else who better understands what the fluid is doing can tackle explaining that.
