Wavelet Analysis of Transitional Flow Data Under High Free-Stream Turbulence Conditions

Transitional flow data from boundary layers subject to strong acceleration (K as high as 9×10⁻⁶) and high free-stream turbulence (∼8%) were analyzed using wavelet transforms. Wavelet analysis provides the energy content of a signal on both a frequency and instantaneous time basis. It differs from traditional Fourier spectral analysis, which can only provide the spectral energy on a time averaged basis. Instantaneous velocity data from intermittent, transitional boundary layers were segregated into turbulent and non-turbulent zones through conditional sampling. Wavelet analysis was used to determine the frequency content of the velocity fluctuations and turbulent shear stress in the two zones separately. The streamwise velocity fluctuations in the turbulent and non-turbulent zones appeared similar. This was attributed to the effect of the free-stream turbulence, which had the same effects on both zones. The wall-normal fluctuations and turbulent shear stress were of significantly higher magnitude and frequency in the turbulent zone. These results suggest that turbulence models should be based on transport quantities rather than turbulent kinetic energy. The regions just upstream and just downstream of turbulent zones were also analyzed, to check for possible important frequencies leading to the initiation of turbulence or characteristic of the “calm” zone trailing a turbulent spot. No distinct behavior was observed in either of these zones. Uncertainty values associated with the wavelet spectra are high due to the short data records available. Results are shown to be valid in spite of these uncertainties, however longer data records should be acquired in future studies.