Integral Invariant of Ideal Gas Flows behind a Detached Bow Shock

We consider a steady flow of an ideal perfect gas formed in a supersonic homogeneous incoming flow behind a detached shock wave in front of a convex body in the general spatial case. The analysis is carried out on the basis of the Euler equations. It is assumed that, in the region between the shock and the convex head part of the streamlined body, the velocity is zero only at the forward stagnation point. Vector lines of vector a , which is the vector product of the velocity and the gradient of the entropy function, are investigated. The study is based on the known property of these lines, which is that they either begin and end on the shock, or are closed. As a result of the study, it is established that a curvilinear integral of the product of the cotangent of angle φ and the temperature, divided by the value of the gas velocity, along any closed vector line a , is equal to zero.