Abstract
The natural frequencies of gravity waves in a circular well that is bounded above by a free surface and below by a semi-infinite reservoir are approximated by neglecting the off-diagonal terms of the characteristic determinant (single-mode approximation) and invoking the known results for an aperture in a half-space (well of zero depth). A parallel argument yields the corresponding results for a two-dimensional well (a slot). Comparison with Molin's (2001) numerical results for a slot suggests that the error in the single-mode approximation is [lsim ] 1%.
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