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This paper presents an analytic solution for the sound generated by anunsteady gust interacting with a semi-infinite flat plate with a serratedleading edge in a background steady uniform flow. Viscous and non-lineareffects are neglected. The Wiener-Hopf method is used in conjunction with anon-orthogonal coordinate transformation and separation of variables to permitanalytical progress. The solution is obtained in terms of a modal expansion inthe spanwise coordinate, however for low- and mid-range incident frequenciesonly the zeroth order mode is seen to contribute to the far-field acoustics,therefore the far-field noise can be quickly evaluated. The solution givesinsight into the potential mechanisms behind the reduction of noise for plateswith serrated leading edges compared to those with straight edges, and predictsa logarithmic dependence between the tip-to-root serration height and thedecrease of far-field noise. The two mechanisms behind the noise reduction areproposed to be an increased destructive interference in the far field, and aredistribution of acoustic energy from low cuton modes to higher cutoff modesas the tip-to-root serration height is increased. The analytic results showgood agreement in comparison with experimental measurements. The results arethen compared against numerical predictions for the sound generated by aspanwise invariant line vortex interacting with a flat plate with serratedleading edge. Good agreement is also seen between the analytical and numericalresults as frequency and tip-to-root ratio are varied.

An Analytic Solution for the Noise Generated by Gust-Aerofoil Interaction for Plates with Serrated Leading Edges