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.