论文标题
通过椭圆征算的零阶伪差异操作员的奇异流的表征：数值研究
Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study
论文作者
论文摘要
分层培养基中内部重力波的传播，例如在海盆和湖泊中发现的介质，导致了几何模式的发展，称为“吸引子”。这些结构积累了大部分波能，并使流体流动高度单数。用更具分析性的术语，这种现象的原因归因于某些非局部零阶伪差异算子中连续频谱的存在。在这项工作中，我们从数值分析的角度分析了这些吸引子的产生。首先，我们提出了一种高阶伪光谱方法来解决进化问题（已知其长期行为不是正方形的行为）。然后，我们使用类似的工具来离散相应的特征值问题。由于特征值嵌入连续频谱中，因此我们使用粘性近似值计算它们。最后，我们探讨了嵌入式本征对系统长期演变的影响。
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make the fluid flow highly singular. In more analytical terms, the cause of this phenomenon has been attributed to the presence of a continuous spectrum in some nonlocal zeroth-order pseudo-differential operators. In this work, we analyze the generation of these attractors from a numerical analysis perspective. First, we propose a high-order pseudo-spectral method to solve the evolution problem (whose long-term behaviour is known to be not square-integrable). Then, we use similar tools to discretize the corresponding eigenvalue problem. Since the eigenvalues are embedded in a continuous spectrum, we compute them using viscous approximations. Finally, we explore the effect that the embedded eigenmodes have on the long-term evolution of the system.
