Triadic instability, vortex cluster, and weak inertial wave turbulence: observations on a wave attractor in an axisymmetric setup

Numerous studies have delved into the properties of inertia-gravity wave reflection, showing in particular that in a confined trapezoidal domain the wave beam experiences a focusing effect, and eventually ends on a limit trajectory called attractor. Evidence of this particular structure have been found in 2D experimental and numerical surveys, and it has been more recently the focus of 3D investigations. Wave attractors are of primordial importance since nonlinear triadic cascades may occur in the branches of the attractor, due to the local energy focusing, leading to energy transfer between scales.

We present experimental and numerical observations of the fate of an axisymmetric inertial wave attractor excited in a fully confined trapezoidal cylindrical domain. Due to focusing and defocusing effects caused by wave reflections and by the radial geometry itself, wave instability occurs while forcing the attractor, eventually leading to an azimuthal symmetry breakdown characterized by the emergence of a regular polygonal vortex cluster. A systematic study of the role of the forcing amplitude, performed using DNS, shows different behaviors: a linear regime, a 3D triadic resonant instability, and a spectral enrichment reminiscent of weak inertial wave turbulence.