Vortex cluster arising from an axisymmetric inertial wave attractor

Abstract

We present an experimental and numerical study of the nonlinear 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 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 nonlinear 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 nonlinear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. This study shows a rich variety of dynamical regimes, including a linear behaviour, a triadic resonance instability, a progressive frequency enrichment reminiscent of weak inertial wave turbulence and the generation of a slow manifold in the form of a polygonal vortex cluster confirming the experimental observation. 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.

Oscillations and Stability of the Jupiter Polar Cyclones

“…Regarding the oscillations, it is reasonable to think that they occur around a hypothetical position of equilibrium and are governed by phenomena akin to those of an elastic force on an object with inertia acting on all 5 cyclones at the South Pole (and presumably also on those at the North). The laboratory model proposed by Boury et al (2021) may indicate a viable mechanism for the oscillations.…”

“…The laboratory model proposed by Boury et al. (2021) may indicate a viable mechanism for the oscillations.…”

“…In these simulations the entrance of a new cyclone into an existing polygonal structure induces a semi‐permanent change in the structure. In laboratory experiments, vortex clusters comparable to the ones observed on Jupiter can emerge spontaneously in a three‐dimensional shallow water setting (Boury et al., 2021) in response to wave‐like perturbations, but a sloped bottom bathymetry such as a conical mountain.…”

Reflections and focusing of inertial waves in a tilted librating cube

“…2014; Sibgatullin & Ermanyuk 2019; Boury et al. 2021) or onto edges or vertices of the container (Greenspan 1969; Beardsley 1970; Troitskaya 2010 a , b ; Wu, Welfert & Lopez 2020).…”

On (n,1) Wave Attractors: Coordinates and Saturation Time

“…Instead, internal wave beams retain their inclination relative to the direction of gravity when reflecting from sloping walls. The importance of wave attractors reveals itself not only in laminar regimes, but also in turbulent ones: even when attractors can not be seen with the "bare eye" and the flow regime looks completely turbulent, the principal pumping of kinetic energy to the system may be realized through the geometric wave attractor [8][9][10][11][12]. Two-dimensional analysis of the internal wave climate over small amplitude random topography [13] shows that in the deep ocean there can be about 10 wave attractors over a thousand kilometer stretch, and most of them are of (n,1) type, having n reflections of horizontal type from both the upper and lower boundary (in which the horizontal direction of the beam does not change upon reflection), and one reflection of vertical type at the left and right ends of the limit cycle.…”