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 (see detachment criterion[1]).
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 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.
The post-shock flow velocity and vorticity can therefore be computed via the Crocco's theorem, which is independent of any EOS (equation of state) assuming inviscid flow.