 Solution

For $\theta >{\theta }_{\max }$, $\gamma \sin \theta >1$, so there is no real solution for an attached straight oblique shock satisfying the assumed geometry. The shock detaches and becomes curved, with a locally strong, nearly normal portion and a subsonic region allowing the flow to adjust to the wall. The precise detached structure depends on the global geometry and downstream conditions; the attached-shock formula cannot be continued to these turns.