Internal Wave Attractors in 3D Geometries : trapping by oblique reflection

TL;DR

This study investigates how internal waves in 3D geometries form attractors through oblique reflection and refractive focusing, revealing mechanisms that trap wave energy and influence wave dynamics in complex environments.

Contribution

It demonstrates the formation of 3D internal wave attractors via oblique reflection and refractive focusing, supported by experiments and numerical simulations, in geometries relevant to natural settings.

Findings

Refractive focusing explains attractor formation across the tank width.

Boundary conditions influence internal wave dynamics and phase shifts.

Wave energy can be trapped in 2D attractors in inclined geometries.

Abstract

We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, 2D parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics,emphasize the role of boundary conditions and reveal the phase shifting in the transversal direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.