Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0

TL;DR

This paper mathematically analyzes how internal and inertial waves in two-dimensional fluids with topography tend to concentrate on attractors, using spectral theory and microlocal analysis, revealing underlying wave dynamics.

Contribution

It provides a rigorous mathematical framework for understanding wave attractors in stratified and rotating fluids, extending previous experimental observations.

Findings

Waves concentrate on attractors in two-dimensional domains with topography.

Spectral theory and microlocal analysis reveal the mechanisms behind wave focusing.

Results apply to both stratified internal waves and inertial waves in rotating fluids.

Abstract

The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In particular, numerical and lab experiments show that, in two dimensions, for generic forcing frequencies, these waves concentrate on attractors. The goal of this paper is to analyze mathematically this behavior, using tools from spectral theory and microlocal analysis. The same results apply also to inertial waves in rotating fluids.