The shock waves are strong perturbations in aerodynamics that propagate at supersonic
speeds independent of the wave amplitude. Such perturbations occur steady transonic
or supersonic flow, lightning strokes, bomb blasts, and contact surfaces in
laboratory devices. The following discussion is limited to common physical
characteristics.

Shocks are classified as weak or strong, depending on the value of the pressure
jump across the shock; they are also classified as normal or oblique, compression or
rarefaction shocks, direct or reflected shocks.

Fig. 1 below shows the progression of the the shock wave and the supersonic pocket on
a conventional airfoil in steady transonic flow.

** Figure 1: Shock Progression on Airfoil**
The shock wave first appears on the suction side and travels slowly toward the
trailing edge (Fig 1a), as the supersonic pocket increases in size. The shock wave on
the lower side appears later (e.g. at higher Mach numbers), but travels faster and
reaches first the trailing edge (Fig 1c). Eventually, also the upper shock wave
reaches the trailing edge, and with the lower shock forms a bifurcated trailing edge
shock (). The thick boundary layer deflects the external flow and creates
compression waves to form the characteristic

### Mathematical Aspects

The jumps of the aero-thermodynamic properties of the gas across a normal shock
are derived from the conservation equations for mass, momentum and energy
(Rankine- Hugoniot).

One approximation that is commonly done is to consider the shock as an insentropic
transformation, which is a good approximation for transonic flows. With the further
approximation of ideal gas, the jumps can be cast in closed form, whose solution
is shown in the graphic below for Mach numbers M < 5.

** Figure 2: Normal shock ratios at supersonic speeds**
#### Oblique Shock

Shocks that are incident at an angle (on a wedge or similar situations) are subject
to a change of direction of the velocity in addition to the features of the normal shock.
The change of direction can be calculated with the full conservation equations, and is
found to be dependent on the density ratio shown in Fig. 2. This change occurs only in
a direction normal to the shock.

The figure below shows the oblique shock waves past a double wedge airfoil at Mach 1.8.
The visualization is a Schlieren photography.

** Figure 3: Double wedge airfoil**