Wave resonances in bounded domains

Apparaît dans la collection : 2026 - T2 - WS3 - Idealised mathematical models for geophysical flows

Nonlinear surface gravity waves sloshing in a container of rectangular cross-section can behave very differently than those with other cross sections. Wave resonance is a mechanism by which energy is continuously exchanged between a small number of wave modes and is common to many nonlinear dispersive wave systems. They have been studied extensively over the past 60-years, almost always on domains that are large (or infinite) compared to the characteristic wavelength. In this case, the dispersion relation dictates that only quartic (4-wave) resonances can occur. In contrast, wave resonances in confined three-dimensional geometries have received relatively little attention, where, perhaps surprisingly, stronger 3-wave resonances of gravity waves can occur. We will present the results characterizing the configuration and dynamics of resonant triads in cylindrical basins of arbitrary cross sections. Extensions to internal waves and other geometries will also be discussed.

Co-authors: Matthew Durey