What Are the Different Exhaust Modes of Rocket Engines During Launch and Flight?

[Clausius2]

When I was viewing some photos about rocket engines (spatial ones), I wondered me in what mode is operating the nozzle in the normal working.I am going to try to explain it better (do not show me a strange face yet). I studied the different exhaust modes of a convergent-divergent nozzle. Depending on the sorrounding pressure the gases will find a normal shock wave inside the nozzle, an oblique shock wave at the outlet, a tangential discontinuty (perfect adapted nozzle), or a Prandtl-Mayer expansion wave. For instance, viewing photos about space-shuttle launch, I have seen the gases being exhausted as a Prandtl Mayer expansion at the solid boosters rockets outlet, but the main engines look like they had an oblique shock wave at their outlet. You can see this observing the external flame far of the nozzle fairing, inside a zone of great pressure I suppose. The structure of the outlet flow of this main engines looks like an oblique shock wave (romboedric), although Enigma could say this more accurately (don't get anger with me if i say something stupid ). In another photograph, the boosters engines of the Soyuz rocket seems to be in Prandtl Mayer expansion regime.
My question is: how does the designers of this rocket engines want to be the type of exhaust at launch and flight?.Does the extreme big pressures reached at combustion chamber make a continuous Prandtl Mayer expansions even at launch?. How it depends on the rocket thrust?. And talking about the visible flame that appears at exhaust of the space shuttle main engines, why is it hanged at such distance of the nozzle fairing? Is in this zone the maximum external pressure?.