Bow shock (aerodynamics)

A bow shock, also called a detached shock or normal shock, is a curved propagating disturbance wave characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density. It occurs when a supersonic flow encounters a body, around which the necessary deviation angle of the flow is higher than the maximum achievable deviation angle for an attached oblique shock. Then, the oblique shock transforms in a curved detached shock wave. As bow shocks occur for high flow deflection angles, they are often seen forming around blunt bodies, because of the high deflection angle that the body impose to the flow around it.
The thermodynamic transformation across a bow shock is non-isentropic and the shock decreases the flow velocity from supersonic velocity upstream to subsonic velocity downstream.
Applications.
The bow shock significantly increases the drag in a vehicle traveling at a supersonic speed. This property was utilized in the design of the return capsules during space missions such as the Apollo program, which need a high amount of drag in order to slow down during atmospheric reentry.
Shock relations.
As in normal shock and oblique shock,