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TsAGI Science Journal

ISSN Druckformat: 1948-2590
ISSN Online: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.2017019463
pages 611-621

SOLVING THE PROBLEM OF SPATIAL DEVELOPMENT OF PERTURBATIONS IN THE LINEAR THEORY OF HYDRODYNAMIC STABILITY BY PHASE FUNCTION MODULATION

Vladimir Aleksandrovich Kuzminsky
Central Aerohydrodynamic Institute (TsAGI) 1, Zhukovsky str., Zhukovsky, 140180, Moscow region, Russia

ABSTRAKT

The linear theory of hydrodynamic stability of three-dimensional compressible flows in a locally parallel approximation is considered. An approach to solving the problem of spatial development of perturbations (the S problem) using phase modulation of the temporal problem solution (the T problem) in the instability region is proposed. It was assumed that the direction of the amplification rate in space coincides with the real part of the group velocity direction in the entire instability region. The obtained transformations of the T problem into the S problem differ from the Gaster transformation. In the extremum of the spatial rate amplification these transformations coincide with the generalized Gaster relation for the three-dimensional case. A comparison was done of the results computed in accordance with the linear stability theory of the frequencies of maximally amplifying unsteady waves of cross-flow instability and the Tollmien−Schlichting waves with the experimental data obtained in the low-turbulent T-124 wind tunnel at TsAGI.


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