# What happens to a shockwave when it goes through different temp/density air?

Specifically I am asking what happens to a shock as it travels through different density air. This answer's comments has some good information about it.

As said in the linked answer, a shock will bend the streamline next to it and extend the shock in doing so, which will also make the streamline next to it bend, which will also continue the shock, then etc etc etc. (read linked answer for a more comprehensive explanation) So knowing that, what does different density air do to this process?

My thinking was that it’d make the streamline trying to bend have some compressibility (higher temp = more compressible air), which would make it so the streamline bent less, which would change the flow turning angle, which would also change the shock angle. That doesn’t really make sense as all the pictures of shocks I’ve seen are straight, even if they traveled through a different temperature/density air.

Something that would answer my question pretty easily: When the shock travels through a different temperature air, does that also make the shock bend?

The closest thing I’ve found on this subject is this Wikipedia article on atmospheric focusing, which touches on this topic slightly.

Higher temperature does not make the air more compressible.

Think of the air in layers.

Assume zero wind -- all the layers of air are still. The thing that is moving (through still air) is the object -- say at 1700 ft/s. Furthermore, the object causes the flow to turn 10 degrees.

At each layer, those things stay the same -- $$V=1700$$ ft/s speed, 10 deg turning.

So, for each layer, find the temperature. From that, calculate the speed of sound.

$$a=\sqrt{\gamma R\, T}$$

Then the Mach number.

$$M=V/a$$

Then look up your shock chart, or use your shock formulas. You know M and the turning angle $$\theta$$, so find the shock angle $$\beta$$.

• Oh okay. So isn’t it easier to compress less dense air compared to denser air. (Here I’m assuming less dense air is higher temperature) Commented Apr 4 at 15:39
• Compressibility from a fluid dynamic standpoint isn't exactly the same thing as putting gas in a bottle with a piston and pushing on the piston. When we talk about a subsonic flow being incompressible vs. a high speed flow being compressible, it isn't an easy/hard thing, it is about how fast the molecules can react to what is happening around it vs. how fast those things are happening. The ratio of the speed of things happening (Velocity) compared to the speed of molecules reacting (speed of sound) is the Mach number. Commented Apr 4 at 16:42
• So in a very real sense, the Mach number is a measure of fluid dynamic compressibility. The speed of sound increases with temperature $a=\sqrt{\gamma R T}$, but from that sense, for the same velocity, hotter air will have a higher speed of sound, a lower Mach number, and will experience less effects from compressibility for an otherwise similar flow. Commented Apr 4 at 16:44
• oh okay, so even though it is more compressible in the sense easier to 'squeeze', the speed of sound is higher so the flow is still able to turn to continue the shock? Commented Apr 4 at 16:52
• Yes, but it is a small effect. Commented Apr 4 at 19:42