# Linear and nonlinear regimes of an inertial wave attractor

## TL;DR

This study experimentally investigates inertial wave attractors in a rotating cavity, revealing linear and nonlinear behaviors, the role of turbulent viscosity, and unexpected resonance instability characteristics influenced by vertical walls.

## Contribution

It introduces a turbulent viscosity model for nonlinear regimes and explores the triadic resonance instability in inertial wave attractors with experimental insights.

## Key findings

- Nonlinear scaling laws can be modeled with turbulent viscosity.
- Triadic resonance instability produces subharmonic waves with unexpected frequencies.
- Vertical walls influence the resonance behavior, deviating from previous theories.

## Abstract

We present an experimental analysis of the linear and non-linear regimes of an attractor of inertial waves in a trapezoidal cavity under rotation. Varying the rotation rate and the forcing amplitude and wavelength, we identify the scaling laws followed by the attractor amplitude and wavelength in both regimes. In particular, we show that the non-linear scaling laws can be well described by replacing the fluid viscosity in the linear model by a turbulent viscosity, a result that could help extrapolating attractor theory to geo/astrophysically relevant situations. We further study the triadic resonance instability of the attractor which is at the origin of the turbulent viscosity. We show that the typical frequencies of the subharmonic waves produced by the instability behaves very differently from previously reported numerical results and from the prediction of the theory of triadic resonance. This behavior might be related to the deviation from horizontal invariance of the attractor in our experiment in relation with the presence of vertical walls of the cavity, an effect that should be at play in all practical situations.