Baroclinic tidal conversion: note on a paper of L.R.M. Maas
Baroclinic tidal conversion: note on a paper of L.R.M. Maas
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DOI：
10.1017/jfm.2022.637
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发表时间：
2022-08
影响因子：
3.7
通讯作者：
C. Wunsch;J. Wunsch
中科院分区：
文献类型：
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作者：
C. Wunsch;J. Wunsch
摘要Maas（J. Fluid Mech.，第684卷，2011年，pp. 5-24）表明，对于流过具有紧密支撑的亚临界地形的振荡二维正压潮，存在一些产生非辐射斜压扰动的地形形式。这个问题与“隐形”和“隐身”问题有关。这里马斯的结果是使用一个更简单的方法，不涉及复杂的映射，但正式限制扰动地形。更广泛的结果来自近紧凑的支持地形的弱高波数辐射的施瓦茨函数提供的干扰，并利用一个已知的功能方程制定和傅立叶方法的讨论。该问题被扩展到均匀斜坡上的扰动。我们可以找到各种各样的非辐射地形，尽管它们在数学上很微妙，不太可能在自然界中找到。在高波数下具有弱辐射的地形是一个更广泛的结构类别。这些解决方案的应用将取决于从远处观察到的运动估计地形上方和附近耗散的能力。
Abstract Maas (J. Fluid Mech., vol. 684, 2011, pp. 5–24) showed that, for an oscillating two-dimensional barotropic tide flowing over sub-critical topography of compact support, some topographic forms existed that produced non-radiating baroclinic disturbances. The problem is related to ‘stealth’ and ‘cloaking’ problems. Here Maas's result is derived using a simpler approach, not involving complicated mappings, but formally restricted to perturbation topography. Wider results come from the discussion of nearly compact support topographic disturbances provided by Schwartz functions with weak high-wavenumber radiation and by exploiting both a known functional equation formulation and Fourier methods. The problem is extended to disturbances on uniform slopes. A variety of non-radiating topographies can be found, although they are mathematically delicate and unlikely to be found in nature. Topography with weak radiation at high wavenumber is a much wider class of structures. Application of these solutions would lie with the ability to estimate dissipation over and near the topography from motions observed at a distance.