Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0

Yves Colin de Verdìère (1) , Laure Saint-Raymond (2)

1 IF - Institut Fourier
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Mots clés: Mourre theory; pseudo-differential operator; attractor; internal waves

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]; Mécanique des fluides [physics.class-ph]

Yves Colin de Verdìère, Laure Saint-Raymond. Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0. Communications on Pure and Applied Mathematics, In press. ⟨hal-01685278v2⟩