Abstract
Standing waves in the cylinder basins with inhomogeneous bottom are considered in this paper. We assume that the inviscid, incompressible fluid is in irrotational undulatory motion. For convenience sake, cylindrical coordinates are chosen. The velocity potentials, the wave profiles and the modified frequencies are determined (to the third order) as power series in terms of the amplitude divided by the wavelength. Axisymmetrical analytical solutions are worked out. When ω1=0,the second order frequency are gained.
As an example, we assume that cylinder bottom is an axisymmetrical paraboloid. We find out that the uneven bottom has influences on standing waves. In the end, we go into detail on geometric factors.
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Yun-li, M., Jia-chun, L. Effects of bottom topography on the standing waves in circular basins. Appl Math Mech 11, 117–124 (1990). https://doi.org/10.1007/BF02014536
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DOI: https://doi.org/10.1007/BF02014536