Reddit reviews Schlieren & Shadowgraph Techniques

I do not think there is water involved; yes it is a "water bottle" but it is a gas inside.

There is nothing inherently special about mach diamonds. It is simply a discontinuity in gas properties. There's a few things at play here:

• Schlieren optics
  
• Pressurized gas
  
  Gas Dynamics
  
  While, yes, you should not be able to accelerate past the sonic condition for the gases entering the converging section of the nozzle; what is stopping the gas from existing at conditions "Mach > 1" relative to the sonic condition of the ambient gases? (This becomes important in reacting flow such as rocket nozzles where the sonic condition of the exhaust products is not the sonic condition of ambient gases).
  
  Shock diamonds will exist when there is a discontinuity in the gas conditions. See: Gas Dynamics References or any book like Gas Dynamics vol. 1 (Zucrow Hoffman) / Fundamentals of Aerodynamics (Anderson). In order to go from the exhaust gas properties to ambient conditions there must be some interface; under certain conditions (M>1) a shock will exist that allows the two states to exist in proximity. For states where (M<1) there is a gradual change between the two conditions dictated by your gas dynamic equations (Navier-Stokes).
  
  Schlieren
  
  Now that we understand why a shock exists; what does Schlieren add? Schlieren optical techniques allow you to see the changes in the refractive index; in the case of gaseous media this translates to density gradients (first derivative), and shadowgraphy lets you see second derivatives. Schlieren & Shadowgraph Techniques (Settles). If you accept that changes in density are related to refractive index, then you can see how Schlieren optical techniques can enhance the viewing of shocks (strong density gradients -- see shock tables and density ratio across a shock). Schlieren techniques can be tuned to REALLY enhance even small density gradients (non-shock environments such as a match, or convective currents around your head -- See Settle's books for good images).