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.

翻译：在分层介质（如海洋盆地和湖泊）中，内重力波的传播会导致出现称为“吸引子”的几何模式。这些结构聚集了大部分波能，使得流体流动高度奇异。从更分析的角度看，这一现象的原因已被归因于某些非局部零阶拟微分算子中存在连续谱。在本研究中，我们从数值分析的角度分析这些吸引子的生成过程。首先，我们提出一种高阶伪谱方法求解演化问题（已知其长期行为并非平方可积）。随后，我们利用类似工具离散化相应的特征值问题。由于特征值嵌入在连续谱中，我们采用黏性近似法计算它们。最后，我们探讨嵌入本征模态对系统长期演化的影响。