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Sloshing in triangular basins
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DOI：10.1016/j.wavemoti.2026.103754.png)
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Abstract
En 中文
We present closed-form sloshing spectra for three uniform-depth triangular basins: the equilateral, the hemi-equilateral, and the right-isosceles triangle. Within linear potential theory, the free-mode problem reduces to a Neumann Helmholtz eigenproblem on the horizontal planform. For each basin we give an explicit real trigonometric eigenbasis and a closed-form expression for the wavenumbers, yielding fully explicit mode shapes and sloshing frequencies through the dispersion relation. To compare geometries on an equal footing, we introduce an area-based normalisation and tabulate the first ten non-zero area-normalised wavenumbers for each basin; the low-lying spectral ordering and interleaving are further illustrated over the first thirty modes. The depth dependence of the fundamental frequency is interpreted via its shallow-and deep-water limits.
Keywords:
Sloshing
Modes
Triangular basin
Helmholtz equation
