Session S33 - Spectral Geometry

Wednesday, July 21, 17:00 ~ 17:20 UTC-3

Internal wave attractors and the spectra of some zeroth-order pseudodifferential operators: a numerical study

Nilima Nigam

Department of Mathematics, Simon Fraser University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The propagation of internal gravity waves in stratified media (such as those found in ocean basins and lakes) leads to the development of attractors. These structures accumulate much of the wave energy and can make the fluid flow highly singular. These questions have been the subject of fascinating recent analytical developments by de Verdière & Saint-Raymond, and Zworski and co-workers.

In joint work with Javier Almonacides, we analyze this phenomenon from a numerical analysis perspective. First, we propose a high-accuracy computational method to solve the evolution problem, whose long-term behaviour is known to be non-square-integrable. Then, we use similar tools to discretize the corresponding eigenvalue problem. Since the eigenvalues are embedded in a continuous spectrum, their computation is based on viscous approximations. Finally, we explore the effect that the embedded eigenmodes have in the long-term evolution of the system.

Joint work with Javier Almonacides (Simon Fraser University, Canada).

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