One singularly perturbed problem of turbulent gas dynamics

A. V. Omel'chenko, È. A. Tropp

St. Petersburg State Polytechnical University, St. Petersburg, 195251

Abstract: The problem of the interaction of a Prandtl–Mayer wave with a shear layer is solved using the small parameter method for the case where the flow vorticity in the shear layer is small. A direct expansion is constructed and its inadequacy at large distances from the vortex layer is proved. The strained coordinate method is used to obtain a uniformly adequate expansion. It is shown that for certain velocity distributions in the shear layer, the characteristics in the reflected simple wave resulting from the interaction intersect each other and a shock arises in the flow. There coordinates of the shock origin and the function describing the shock shape are obtained.

Keywords: simple-wave interaction, gas dynamics, asymptotic expansions, singular problem.

UDC: 533.6.011.72

Received: 24.10.2003

 English version: Journal of Applied Mechanics and Technical Physics, 2004, 45:2, 187–198

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