Editing Compressible flow (section)

===Oblique shock waves===
{{Main|Oblique shock}}
[[File:Oblique Shock Wave.JPG|thumb|Diagram of obstruction]]
Oblique shock waves are similar to normal shock waves, but they occur at angles less than 90° with the direction of flow.  When a disturbance is introduced to the flow at a nonzero angle (δ), the flow must respond to the changing boundary conditions. Thus an oblique shock is formed, resulting in a change in the direction of the flow.

====Shock polar diagram====
[[File:Shock polar diagram.jpg|thumb|Shock polar diagram]]
Based on the level of flow deflection (δ), oblique shocks are characterized as either strong or weak. Strong shocks are characterized by larger deflection and more entropy loss across the shock, with weak shocks as the opposite. In order to gain cursory insight into the differences in these shocks, a shock polar diagram can be used. With the static temperature after the shock, T*, known the speed of sound after the shock is defined as,
:<math> A^* = \sqrt{\gamma RT^*} </math>

with R as the gas constant and γ as the specific heat ratio. The Mach number can be broken into Cartesian coordinates
:<math>\begin{align}
  M^*_{2x} &= \frac{V_x}{a^*} \\
  M^*_{2y} &= \frac{V_y}{a^*}
\end{align}</math>

with V<sub>x</sub> and V<sub>y</sub> as the x and y-components of the fluid velocity V. With the Mach number before the shock given, a locus of conditions can be specified. At some {{not a typo|δ<sub>max</sub>}}, the flow transitions from a strong to weak oblique shock. With δ = 0°, a normal shock is produced at the limit of the strong oblique shock and the Mach wave is produced at the limit of the weak shock wave.

====Oblique shock reflection====
Due to the inclination of the shock, after an oblique shock is created, it can interact with a boundary in three different manners, two of which are explained below.

=====Solid boundary=====
Incoming flow is first turned by angle δ with respect to the flow. This shockwave is reflected off the solid boundary, and the flow is turned by – δ to again be parallel with the boundary. Each progressive shock wave is weaker and the wave angle is increased.

=====Irregular reflection=====
An irregular reflection is much like the case described above, with the caveat that δ is larger than the maximum allowable turning angle. Thus a detached shock is formed and a more complicated reflection known as Mach reflection occurs.