2D internal waves in an ergodic setting

2023/01/29 by Zhenhao Li, Li, Zhenhao · 1 citation
Computer Science · Earth and Planetary Sciences · #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Oceanographic and Atmospheric Processes

paper · pdf · doi:10.48550/arxiv.2301.12365

openalex publication_date 2023/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a model of internal waves under periodic forcing in an effectively 2-dimensional aquarium. When the underlying classical dynamics has sufficiently irrational rotation number, we prove that the solution to the internal waves equation remains bounded in energy space in time. This result is in contrast with the works by Colin de Verdière--Saint-Raymond and Dyatlov--Wang--Zworski, which gave a description of singular profiles when the underlying dynamics has periodic attractors. Our result is proved by showing the spectral measure near the forcing frequency is very small.

Cited by

• Evolution of internal waves in a 2D subcritical channel

Related

• Internal waves in aquariums with characteristic corners
• Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0
• Evolution of internal waves in a 2D subcritical channel
• An Evans-Function Approach to Spectral Stability of Internal Solitary Waves in Stratified Fluids
• On internal wave whispering gallery modes in channels and critical-slope wave attractors