Stokes waves revisited: Exact solutions in the asymptotic limit
Stokes waves revisited: Exact solutions in the asymptotic limit
复制标题
重温斯托克斯波：渐近极限的精确解
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
A. Chattopadhyay
中科院分区：
文献类型：
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作者：
M. Davies;A. Chattopadhyay
翻译后摘要：斯托克斯微扰解的非线性（边界值相关）表面重力波问题是已知的，以提供合理的精度的结果，工程师在估计这种非线性波的相速度和振幅。然而，这种结构的弱点是解中存在非周期性的“长期变化”，这与已知的表面波周期传播不一致。这在历史上需要越来越高阶（微扰）的近似表示的速度分布。本文通过在渐近无限深度极限中调用紧凑的精确n阶解来改善这种长期存在的理论不足，主要基于围绕三阶微扰解构造的表示，这导致无缝扩展到高阶（例如，第五章文献中存在的问题这项研究的结果预计将改善唯象工程估计，现在，任何所需的高阶扩展可以在同一表示内压缩，但没有任何非周期性的光谱图案的波导。
Abstract.The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.