发表机构
California Institute of Technology（加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究海岸捕获波的正交性，通过将$f$平面上的静水Boussinesq动力学表述为广义薛定谔方程，转化为有限元离散化来保留对称性，还讨论了地转动量近似，强调低频海岸捕获波是边缘波，其动力学受边界位势涡度异常控制。
AI 中文摘要
海岸捕获波模式在对波场能量做出独立贡献的意义上被证明是正交的。在静止状态附近线性化的$f$平面上的静水Boussinesq动力学被表述为一个（广义）薛定谔方程，这揭示了波算子的厄米结构，意味着本征模的正交性。这种表述在弱形式下特别简单，被转化为有限元离散化，保留了原始问题的对称性，从而保留了模式的能量守恒和正交性。以前已经认识到模式正交性的地转动量近似在本文中被重新讨论，以强调低频海岸捕获波是边缘波。它们的动力学由边界位势涡度异常控制，包括准地转方程中熟悉的布雷瑟顿型贡献以及对陡坡和海岸壁很重要的横向贡献。
英文摘要
Coastal trapped wave modes are shown to be orthogonal in the sense that they make independent contributions to the energy of the wave field. The hydrostatic Boussinesq dynamics on an $f$-plane, linearized around a state of rest, are formulated as a (generalized) Schrödinger equation, which exposes the Hermitian structure of the wave operator that implies the orthogonality of eigenmodes. This formulation, which becomes particularly simple in weak form, is parlayed into a finite-element discretization that preserves the symmetries of the original problem and therefore the energy conservation and orthogonality of modes. The geostrophic momentum approximation, under which the orthogonality of modes has been recognized previously, is reprised and discussed in the present context to emphasize that low-frequency coastal trapped waves are edge waves. Their dynamics are governed by boundary potential-vorticity anomalies, both Bretherton-type contributions familiar from the quasi-geostrophic equations and lateral contributions that are important for steep slopes and coastal walls.
Journal refJournal of Physical Oceanography 56 (2026), 2391-2403
