On the Value of the Second Invariant of the Strain Rate Tensor at the Point of Minimum Pressure on the Plane of Symmetry of Non-Barotropic Flow

Abstract

In this paper, we consider a nonbarotropic vortex flow of an ideal gas symmetric with respect to some plane. Using the Euler equations for stationary flows, it is established that if the pressure reaches a strict or nonstrict local minimum at an internal point of the flow located on the plane of symmetry, the flow is subsonic at this point, and the velocity is nonzero, then the value of the Q parameter at this point must be equal to zero. It is also established that if at the considered point a local minimum or maximum of pressure is reached not in space, but only in the symmetry plane, then the value of the Q parameter must be nonpositive. The last statement turns out to be true both for subsonic and for sonic and supersonic points. The results can be used to verify numerical calculations of an ideal gas flow behind a detached shock wave in a supersonic flow around symmetric bodies, as well as numerical calculations of a viscous gas flow around symmetric bodies in regions remote from vorticity sources, where the effect of viscosity and thermal conductivity can be neglected.