Edge waves on a sloping beach
Edge waves on a sloping beach
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DOI：
10.1098/rspa.1952.0152
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发表时间：
1952-08
期刊：
影响因子：
--
通讯作者：
F. Ursell
中科院分区：
文献类型：
--
作者：
F. Ursell
机械系统的特征频率集形成其频谱。讨论了具有离散、连续和混合光谱的系统。结果表明，共振发生在频谱的离散点和截止频率（连续频谱的端点）。由倾斜海滩封闭的有限宽度的半无限运河中的运动具有混合频谱。无粘性理论预测，在离散频率下，共振仅限于海滩附近（无粘性边缘波），而在截止频率下，共振会沿着运河延伸很长一段距离。后者的共振通过粘性被限制在海滩附近（粘性边缘波），粘性在截止频率附近很重要。预计一系列临界角会产生特别大的共振，其中最大的临界角为 30°。该理论在 100 至 17c/min 的频率范围内，角度 37⋅6 和 29⋅5° 得到了实验验证。
The set of eigenfrequencies of a mechanical system forms its spectrum. A discussion is given of systems with discrete, continuous and mixed spectra. It is shown that resonance occurs at discrete points of the spectrum, and at cut-off frequencies (end-points of the continuous spectrum). The motion in a semi-infinite canal of finite width closed by a sloping beach has a mixed spectrum. The inviscid theory predicts that at a discrete frequency the resonance is confined to the neighbourhood of the beach (inviscid edge wave), while at a cutoff frequency the resonance extends a long way down the canal. The latter resonance is confined to the neighbourhood of the beach (viscous edge wave) by viscosity which is important near a cut-off frequency. Especially large resonances are predicted for a series of critical angles, of which the largest is 30°. The theory is verified experimentally in the frequency range 100 to 17c/min for the angles 37⋅6 and 29⋅5°.