Nonuniqueness of the Transonic Flow past an Airfoil

The inviscid transonic flow past a symmetric airfoil having a curvature minimum in the middle is numerically investigated. It is shown that at zero angle of attack both symmetric and asymmetric steady-state flow patterns can exist on a certain freestream Mach number range M_min < M_max. On this range, the asymmetric flows are stable against small perturbations, whereas the symmetric flows are stable only if M does not coincide with a singular Mach number at which small variations in M or can result in flow restructuring.