fluid dynamics - Intuitive explanation of supersonic flow behavior?

It is well known that once the flow of a gas becomes supersonic, it behaves very differently to subsonic flow:

• Velocity increases as flow area increases.


• Velocity decreases along a pipe with friction.


• Velocity decreases if a flow is heated externally.

The opposite is true for all of these in the case of subsonic flow.

I am familiar with the mathematical explanations that go through several pages of 1D compressible flow theory; however, I struggle to understand intuitively why a supersonic flow behaves so differently to a subsonic flow, in the sense that it practically reverses in behavior like this.

Does anyone know of a good, intuitive explanation as to why supersonic flows behave like this (beyond just: 'it does, because the math says so')?