An infinitely long canal with uniform cross-section S is filled with an ideal fluid which supports surface waves of small amplitude and wavelength. The curve S intersects the free surface vertically and is taken to be smooth and non-planar at these points. The object of this work is to find the asymptotic behaviour of the normal mode solutions in the short wave limit ϵ/a → 0, where ϵ is a measure of the wavelength and 2a the canal width. The method of matched asymptotic expansions is used. As a first approximation φ o , to be valid many wavelengths from the surface, the free surface condition is replaced by its formal limit φ o = 0. Near the points of intersection of the free surface and the canal walls however, the correct free surface condition is used, but the geometries of the walls are simplified. Finally the approximation φ o is extended to cover the remaining surface layers by adding to it wave-trains of suitable amplitude, and the eigenvalues ϵ m are estimated asymptotically.
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