Question

According to Crocco’s theorem, the vorticity behind the curved shockwave is zero.

(a) True

(b) False

This question was posed to me in an international level competition.

My doubt is from Crocco’s Theorem topic in portion Differential Conservative Equations for Inviscid Flow of Aerodynamics

Answer 1

Correct option is (b) False

To explain: Across a stationary shock wave, the change in enthalpy is zero therefore ∇s = 0. But for a curved shockwave, the enthalpy does not remain constant making ∇s ≠ 0. This results in V × (∇ × V) ≠ 0 according to the Crocco’s theorem. Therefore the vorticity behind a curved shock wave is not zero and the flow behind the curved shock wave is rotational.