Gas turbines actually have varying efficiencies against reciprocating engines, depending on the designs being compared. In the overlap area of small turbines and large pistons, pistons win out significantly in HP per fuel rate. Turbines do have higher power/weight as you say though. This Wave engine's pretty different as it features centrifugal versus axial flow (ironically, the first turbines developed by the US/UK attempted centrifugal designs - the germans gave us our modern axial flow jet engines).
A shock contacting the metal isn't a big deal. A typical jetliner will have a standing shock on the upper surface of its wing during cruise flight, visible if the lighting is just right. With this I doubt there will be significant stresses caused by the pressure gradient because the thing is pretty much a compact and flat disk (short moment arms).
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Gas turbines actually have varying efficiencies against reciprocating engines, depending on the designs being compared. In the overlap area of small turbines and large pistons, pistons win out significantly in HP per fuel rate. Turbines do have higher power/weight as you say though. This Wave engine's pretty different as it features centrifugal versus axial flow (ironically, the first turbines developed by the US/UK attempted centrifugal designs - the germans gave us our modern axial flow jet engines).
A shock contacting the metal isn't a big deal. A typical jetliner will have a standing shock on the upper surface of its wing during cruise flight, visible if the lighting is just right. With this I doubt there will be significant stresses caused by the pressure gradient because the thing is pretty much a compact and flat disk (short moment arms).