Effects of Bottom Topography on the Standing Waves in Circular Basins

Standing waves in the cylinder hasins 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 velocitv 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 axisymmetricat paraboloid.We find out that the uneven bottom has influences on standing waves.In the end.we go into detail on geometric factors.