底部形状对圆柱形港池中驻波的影响

本文用摄动法讨论了具有不规则底部的圆柱形港池中的驻波.假设流体是无粘性、不可压、无旋的.为方便起见,采用柱坐标系.速度势、波形以及频率均以相应于振幅的小参数进行摄动展开,获得了轴对称波驻的分析解,当ω₁=0时,算出了二阶频率.作为一个算例,取圆柱体底部为一轴对称抛物面,算出这种不规则底部对驻波产生灼影响.最后,对几何因素的影响进行了详细的讨论.

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.