Recognition of Tollmien-Schlichting waves excited by acoustic disturbances using discrete wavelet transform

Localized acoustic receptivity experiments are conducted on a two-dimensional flat plate in a low-turbulence wind tunnel. Discrete wavelet transform (DWT) is employed to detect and identify Stokes waves and Tollmien-Schlichting (T-S) waves within the boundary layer. The effects of disturbance frequency and roughness thickness on the amplitude of T-S waves are examined separately in a low-speed regime. The phase velocities of the T-S waves at each measurement location are validated and found to be in good agreement with theoretical predictions. Additionally, the velocity profiles of both T-S and Stokes waves closely matches those predicted by linear stability theory. Time-frequency analysis of the DWT signals is performed using the short-time Fourier transform, revealing a narrow frequency bandwidth. The error between the peak frequency of the T-S waves and the forcing frequency is found to be less than 5%. Local receptivity coefficients are estimated using an extrapolation method, which shows that at a dimensionless forcing frequency of 79.92, the receptivity growth rate in the streamwise direction is higher compared to that at a dimensionless frequency of 99.90. This novel method offers a more precise recognition of T-S waves, simplifying the measurement process compared to traditional pulsed sound techniques. It eliminates the need for ensemble averaging based on repeated measurements and improves the frequency resolution of the T-S waves.