Vortex cluster arising from an axisymmetric inertial wave attractor
Résumé
We present an experimental and numerical study of the non-linear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The rotating ring-shaped fluid domain is delimited by two vertical coaxial cylinders, a conical bottom, and a horizontal wave generator at the top: the vertical cross-section of the fluid volume is a trapezium, while the horizontal cross-section is a ring. Forcing is introduced via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. The experiment shows an important result: at sufficiently strong forcing and long time scale, a saturated fully non-linear regime develops as a consequence of an energy transfer draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially-oriented cyclonic vortices undergoing a slow prograde motion around the inner cylinder. We explore the long-term non-linear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. We observe a rich variety of dynamic regimes, including a linear behaviour, a Triadic Resonance Instability (TRI), a progressive frequency enrichment reminiscent of weak inertial Wave Turbulence (WT), and the generation of a slow manifold in the form of a Polygonal Vortex Cluster (PVC). This vortex cluster is discussed in detail, and we show that it stems from the summation and merging of wave-like components of the vorticity field. The nature of these wave components, the possibility of their detection under general conditions and the ultimate fate of the vortex clusters at even longer time scale remain to be explored.
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