  Serrations are commonly employed to mitigate the turbulent boundary layer
trailing-edge noise. However, significant discrepancies persist between model
predictions and experimental observations. In this paper, we show that this
results from the frozen turbulence assumption. A fully-developed turbulent
boundary layer over a flat plate is first simulated using the large eddy
simulation (LES) method, with the turbulence at the inlet generated using the
digital filter method (DFM). The space-time correlations and spectral
characteristics of wall pressure fluctuations are examined. The simulation
results demonstrate that the coherence function decays in the streamwise
direction, deviating from the constant value of unity assumed in the frozen
turbulence assumption. By considering an exponential decay function, we relax
the frozen turbulence assumption and develop a prediction model that accounts
for the intrinsic non-frozen nature of turbulent boundary layers. To facilitate
a direct comparison with frozen models, a correction coefficient is introduced
to account for the influence of non-frozen turbulence. The comparison between
the new and original models demonstrates that the new model predicts lower
noise reductions, aligning more closely with the experimental observations. The
physical mechanism underlying the overprediction of the noise model assuming
frozen turbulence is discussed. The overprediction is due to the decoherence of
the phase variation along the serrated trailing edge. Consequently, the ratio
of the serration amplitude to the streamwise frequency-dependent correlation
length is identified as a crucial parameter in determining the correct
prediction of far-field noise.
