  A new analytical model is developed for the prediction of noise from serrated
trailing-edges. The model generalizes Amiet's trailing-edge noise theory to
sawtooth trailing-edges, resulting in an inhomogeneous partial differential
equation. The equation is then solved by means of a Fourier expansion technique
combined with an iterative procedure. The solution is validated through
comparison with finite element method for a variety of serrations at different
Mach numbers. Results obtained using the new model predict noise reduction of
up to 10 dB at 90 degree above the trailing-edge, which is more realistic than
predictions based on Howe's model and also more consistent with experimental
observations. A thorough analytical and numerical analysis of the physical
mechanism is carried out and suggests that the noise reduction due to serration
originates primarily from interference effects near the trailing-edge. A closer
inspection of the proposed mathematical model has led to the development of two
criteria for the effectiveness of the trailing-edge serrations, consistent but
more general than those proposed by Howe. While experimental investigations
often focus on noise reduction at ninety degrees above the trailing-edge, the
new analytical model shows that the destructive interference scattering effects
due to the serrations cause significant noise reduction at large polar angles,
near the leading edge. It has also been observed that serrations can
significantly change the directivity characteristics of the aerofoil at high
frequencies and even lead to noise increase at high Mach numbers.
