Mathematical Analysis of Continental Shelf Waves on a Curved Coast

弯曲海岸上大陆架波的数学分析

• 批准号: EP/D054621/1
• 负责人: Michael Levitin
• 金额: $ 18.68万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD054621%2F1
• 关键词: Mathematical; Analysis; Continental; Shelf; Waves

Measurements of velocity fields along the coasts of oceans throughout the world show that much of the fluid energy is contained in motions with periods of a few days or longer. The comparison of measurements at different places along the same coast show that in general these low-frequency disturbances propagate along coasts with shallow water to the right in the northern hemisphere and to the left in the southern hemisphere. These waves have come to be known as continental shelf waves (CSWs). The purpose of the present proposal is to determine, using a selection of models of increasing complexity, the form of non-propagating, trapped CSWs along curved coasts. The existence of such non-propagating modes is significant as they would tend to be forced by atmospheric weather systems, which have similar periods of a few days, similar horizontal extent, and a reasonably broad spectrum in space and time. Areas where such modes were trapped would thus appear to be likely to show higher than normal energy in the low frequency horizontal velocity field.

对世界各地海洋沿岸速度场的测量表明，大部分流体能量包含在周期为几天或更长时间的运动中。对同一海岸不同地方的测量结果的比较表明，一般来说，这些低频扰动沿着北半球的浅水海岸向右传播，在南半球向左传播。这些波被称为大陆架波（CSWs）。本提案的目的是利用一系列日益复杂的模型来确定沿弯曲海岸非传播的、被困的CSWs的形式。这种非传播模态的存在意义重大，因为它们往往受到大气天气系统的影响，而大气天气系统具有相似的几天周期、相似的水平范围和在空间和时间上相当广泛的频谱。因此，这些模式被捕获的区域在低频水平速度场中可能显示出比正常能量更高的能量。

项目成果

A PT-symmetric periodic problem with boundary and interior singularities

具有边界和内部奇点的PT对称周期问题

• 发表时间: 2010
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: L Boulton

A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

计算具有无限规则末端的域中特征值和共振的简单方法

• 发表时间: 2008
• 期刊: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
• 影响因子: 1.3
• 作者: Levitin Michael

On a class of non-self-adjoint periodic boundary value problems with discrete real spectrum

一类离散实谱非自伴周期边值问题

• 发表时间: 2010
• 作者: L Boulton