The instability regimes of transonic flow over an airfoil
Matematičeskoe modelirovanie, Tome 16 (2004) no. 11, pp. 101-106

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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.
@article{MM_2004_16_11_a8,
     author = {D. S. Semyonov},
     title = {The instability regimes of transonic flow over an airfoil},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {101--106},
     publisher = {mathdoc},
     volume = {16},
     number = {11},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_11_a8/}
}
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D. S. Semyonov. The instability regimes of transonic flow over an airfoil. Matematičeskoe modelirovanie, Tome 16 (2004) no. 11, pp. 101-106. http://geodesic.mathdoc.fr/item/MM_2004_16_11_a8/