Internal waves in 2D aquaria
Organizers
Xi Chen
,
Long Jin
Speaker
Maciej Zworski
Time
Friday, March 25, 2022 10:00 AM - 11:00 AM
Venue
1129B
Online
Zoom 618 038 6257
(SCMS)
Abstract
The connection between the formation of internal waves in fluids, spectral theory, and homeomorphisms of the circle was investigated by oceanographers in the 90s and resulted in novel experimental observations (Maas et al, 1997). The specific homeomorphism is given by a ``chess billiard" and has been considered by many authors (John 1941, Arnold 1957... ). The relation between the nonlinear dynamics of this homeomorphism and linearized internal waves provides a striking example of classical/quantum correspondence (in a
classical and surprising setting of fluids!). I will illustrate the results with numerical examples and explain how classical concepts such as rotation numbers of diffeomorphisms (introduced by Poincare) are related to solutions of the Poincare evolution problem. The talk is based on joint work with S Dyatlov and J Wang.