Davis has shown by means of a lengthy calculation that, for two-dimensional oscillations in a canal of width 2a, the mth eigenvalue has the form \[ N_m = {1/2}mπ - λ_1+λ_2/4mπ+o(1/m), \] where λ1/a and λ2/a are the curvatures of the bounding cross-sectional curve C at its vertical intersections with the free surface. Here the same result is obtained more simply.
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F. Ursell (1974) studied this question.
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