Mathematical Sciences: Nonlinear Coupling of Solitary Internal Waves With Small- Scale Disturbances

数学科学：孤立内波与小尺度扰动的非线性耦合

• 批准号: 9202064
• 负责人: Triantaphyllos Akylas
• 金额: $ 13.76万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1995-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202064&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Coupling; Solitary

Solitary internal waves are common features in the ocean, due to existing temperature and salinity variations, and play an important part in the transport of energy and momentum. Our current theoretical understanding of internal solitary-wave dynamics is based, to a large extent, on weakly nonlinear long- wave theories which are derived on the assumption that only long waves are present. On the other hand, there is evidence from laboratory and field observations that, in general, large- amplitude solitary internal waves do not remain locally confined as suggested by these approximate theories, but, rather, they develop short-wavelength oscillatory tails that cause radiation damping. This radiation, in turn, provides a nonlinear mechanism for coupling large-amplitude solitary-wave disturbances with short-scale oscillatory waves of different modes. For example, it is possible for solitary internal waves to transfer energy to short-scale surface waves that remain phase-locked with the internal waves P a situation reminiscent of the surface rips that often accompany internal waves in the field, and are visible in radar images of the sea surface. In order to fill the gap currently existing in our theoretical understanding, this research program investigates the generation of oscillatory tails and the related radiation- dampling mechanism of solitary internal waves, using singular- perturbation and numerical methods. Particular emphasis is placed on calculating the amplitude of short-wave tails under realistic conditions, including the possibility of deep fluids and the presence of a free surface. For this purpose, a nonlinear WKB technique will be developed for weakly nonlinear disturbances, and fully numerical computations will be carried out for large-amplitude solitary waves. In addition, the transfer of energy from solitary waves to small-scale disturbances of different modes (short-scale surface or lower- mode internal waves) will be examined in comparison with other physical processes, like viscous dissipation, that occur in practice.

孤立内波是海洋中的常见特征， 由于现有的温度和盐度变化， 是能量和动量传递的重要组成部分。 我们 内孤立波理论研究现状 动力学在很大程度上是基于弱非线性长- 波浪理论是基于只有长的 波是存在的。 另一方面，有证据表明， 实验室和现场观察，一般来说，大- 振幅孤立内波不会保持局部限制 正如这些近似理论所建议的那样，但是，相反，他们 形成短波长的振荡尾巴， 阻尼 这种辐射反过来又提供了一种非线性的 大振幅孤波耦合机制 短尺度振荡波扰动 modes. 例如，孤立内波 将能量转化为短尺度的表面波 与内波P相位锁定，这种情况让人想起 表面撕裂，往往伴随着内波在 在海面的雷达图像中可见。 为了填补我国目前存在的差距， 理论理解，本研究计划调查 振荡尾巴的产生和相关的辐射- 孤立内波的阻尼机制，使用奇异- 扰动和数值方法。 特别强调 放置在计算短波尾巴的振幅下， 现实条件，包括深层流体的可能性 以及自由表面的存在。 为此，A 非线性WKB技术将发展为弱非线性 干扰，并进行完全数值计算， 大振幅孤立波。 此外该 孤立波向小尺度的能量传递 不同模式的扰动（短尺度表面或低尺度表面）， 模式内波）将检查与其他 物理过程，如粘性耗散，发生在 实践