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The trapping of surface waves above a submerged, horizontal cylinder

The existence of surface waves trapped above a submerged horizontal cylinder was shown by Ursell to depend upon the vanishing of a certain infinite determinant. Here, the determinant is evaluated numerically and the dispersion curves found. It is shown that the mild slope equation may be used to determine the dispersion relation and surface profiles with good accuracy and with less computational effort than the full linear theory.