Short surface waves in a canal: dependence of frequency on curvature
A. M. J. Davis · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1969
Abstract In a previous paper concerning two-dimensional oscillations in a canal, the asymptotic form of the mth eigenvalue of N (= σ2a/g) was shown to be ½mπ+O(1/m). Here the coefficient of 1/m is calculated in terms of the curvatures of the bounding cross-sectional curve C at its vertical intersections with the free surface. The accuracy of the approximation is tested by computing eigenvalues for the case when C is a semicircle.