Transient and steady-state amplitudes of forced waves in rectangular basins
Transient and steady-state amplitudes of forced waves in rectangular basins
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DOI：
10.1063/1.1569917
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发表时间：
2003-05
影响因子：
4.6
通讯作者：
D. Hill
中科院分区：
文献类型：
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作者：
D. Hill
提出了矩形盆地中二维驻波瞬态演化的弱非线性分析。波通过沿着与波数矢量对齐的轴的周期性振荡而产生共振。相对于盆地尺寸，假设振荡幅度较小。同时考虑失谐、粘性阻尼和三次非线性的影响。此外，该分析是在一般深度的水中进行的。使用多尺度分析来推导谐振波复振幅的演化方程。根据该方程，可以确定波的最大瞬态和稳态幅度。结果表明，稳态分析会低估盆地从静止状态开始运动的最大响应。振幅响应图表明与之前的实验研究具有良好的一致性。该分析在“临界深度”附近和浅水极限处无效。一个单独的...
A weakly-nonlinear analysis of the transient evolution of two-dimensional, standing waves in a rectangular basin is presented. The waves are resonated by periodic oscillation along an axis aligned with the wavenumber vector. The amplitude of oscillation is assumed to be small with respect to the basin dimensions. The effects of detuning, viscous damping, and cubic nonlinearity are all simultaneously considered. Moreover, the analysis is formulated in water of general depth. Multiple-scales analysis is used in order to derive an evolution equation for the complex amplitude of the resonated wave. From this equation, the maximum transient and steady-state amplitudes of the wave are determined. It is shown that steady-state analysis will underestimate the maximum response of a basin set into motion from rest. Amplitude response diagrams demonstrate good agreement with previous experimental investigations. The analysis is invalid in the vicinity of the “critical depth” and in the shallow-water limit. A separat...