The instability regimes of transonic flow over an airfoil

A numerical simulation of inviscid transonic flow over symmetric airfoils is carried out. As shown, there exist both symmetric and nonsymmetric steady flow patterns in a range of freestream velocities at the vanishing incidence. The nonsymmetric patterns are stable with respect to small perturbation of the angle of attack and the freestream Mach number $M_\propto$. The symmetric flow is stable if $M_\propto$ does not coincide with a singular Mach number that depends on the airfoil under consideration.