  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.
