Super to Subcritical, and Super to Subsonic Flow

[Clausius2]

My aim in this thread is to bring light to the physical foundations of the next event.

1) Assume there is a long open channel filled with water. Due to some difference of height between its extremes, there is an steady flow of water. Imagine there is an smooth obstacle of height z_o (like a small and smooth hill) in the middle of the channel. Because of open channel flow theory we know that if the flow is subcritical upstream the obstacle and if the obstacle has enough peak height z_o then it would be possible (not necessary) to have supercritical flow behind it.

Now assume there is supercritical flow upstream the obstacle (with supercritical flow I mean Froude number is larger than unity F_r>1 and the contrary for subcritical flow). My question is: would it be possible to obtain subcritical flow just downstream the obstacle without the presence of an hydraulic jump?

Those who don't know nothing about open channel flow could answer to this another similar question. Imagine a convergent-divergent nozzle in which inlet there is supersonic flow. Assuime the inlet flow is free of shock waves. Now the flow enters the nozzle and because of the reduction of section the flow is being slowed down progressively until it reaches the critical section (minimum area) where the flow is sonic. Once it enters the divergent section, the flow could be deccelerated to subsonic flow due to the dynamic diffusing effect. So that we will have a global transition of supersonic to subsonic flow without the presence of a shock wave. Is it possible?.

I have some more questions about physics of open channel flow, but I'll wait for some brave guy who wants to give me some opinion of these.

Regards,

Javier.

 

[minger]

I'm not an expert or even somewhat knowledgeable in these matters, but...I thought that if you had a convergent-divergent nozzle and flow reached sonic at the throat, then it would accelerate back up where it diverges (nozzles diverge for sonic,supersonic, diffusers converge, opposite of subsonic)

 

[Clausius2]

I'm not an expert or even somewhat knowledgeable in these matters, but...I thought that if you had a convergent-divergent nozzle and flow reached sonic at the throat, then it would accelerate back up where it diverges (nozzles diverge for sonic,supersonic, diffusers converge, opposite of subsonic)

This event could be possible too. The fact is when there are critical conditions just at the throat it can be a sudden transition to anyone of the regimes.

My actual question is if a convergent-divergent nozzle could decelerate a supersonic stream to a subsonic one without any shock wave, merely by the same principle of how it accelerates a subsonic stream to a supersonic one. Would it be mathematically and physically possible such a smooth transition?