Measurements of the unsteady mass flux deficit of a turbulent spot: implications for boundary layer transition noise

Unsteady velocity field measurements of an isolated, artificially generated turbulent spot were made in a zero-pressure gradient laminar boundary layer in a water channel facility. These measurements were used to provide quantitative information concerning the local large-scale boundary layer displacement thickness fluctuations due to the passage of a turbulent spot, which are believed to be an important sound source mechanism in boundary layer transition. Ensemble averaging of the velocity data was triggered on the spot generation. The unsteady mass flux deficit (MFD) was calculated from the ensemble-averaged velocity data taken at five streamwise (x) locations. At each location the amplitudes of the peaks in both the unsteady MFD and the unsteady velocity normal to the plate (v_n), as well as the characteristic MFD rise times, t_i, were deduced from the MFD time series. Comparing the results at different stations shows that t_i and the peak MFD amplitude increases with x, while the peak amplitude of V_n increases early in the spot development, but reaches a maximum. For all these parameters, the rate of spatial growth is greatest in the most upstream portions of the boundary layer. The normalized rise time, U_ct_iΔX, introduced by Lauchle (1981), was found to span a range of values 0.06 < U_ct_iΔx < 0.74 over the locations we measured, with the lowest values again in the upstream end of the transition zone. Scaling analysis using these experimental results shows that the sound radiated by the large-scale motion due to an isolated turbulent spot increases as the spot grows and has a dipole character. Extrapolation to a natural transition zone indicates that sound radiation from the large-scale intermittent motion is highest in the middle part of the transition zone because the spot density is highest there.