Resonant interactions of Tollmien-Schlichting waves in the boundary layer on a flat plate

Abstract

Resonant interaction phenomena of Tollmien-Schlichting waves (T.-S. waves) are examined experimentally by spectral analysis method. Results demonstrate that, in the spectra measured in the vicinity of the critical layer of the unstable boundary layer, the energy of T.-S. waves concentrates in a narrow band of frequency with one to three peaks in the power spectra corresponding to the eigenfrequencies of T.-S. waves and the frequency with maximum growth rate located between the upper and lower branches of the neutral curve. The resonant interactions transfer the energy of these eigencomponents to their subsequent subharmonics in a range ofR _δ* where their growth rates increase from zero to a maximum value, and the boundary layer becomes turbulent after the third resonant interaction.