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.

中文翻译：

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由轴对称惯性波吸引子产生的涡簇

我们对轴对称几何设置中惯性波吸引子的非线性动力学进行了实验和数值研究。旋转环形流体域由两个垂直的同轴圆柱体、锥形底部和顶部的水平波发生器界定：垂直截面为梯形，而水平截面为环形。强迫是通过上眼睑的轴对称低振幅体积守恒振荡运动引入的。实验显示了一个重要的结果：在足够强的强迫和长时间尺度下，饱和的完全非线性状态是由于能量转移向缓慢的二维流形消耗能量的结果，该流形由轴向气旋涡旋的正多边形系统表示。围绕内圆柱的缓慢前进运动。我们通过对一组固定的强迫幅度进行一系列数值模拟来探索系统的长期非线性行为。这项研究显示了多种动力学状态，包括线性行为、三元共振不稳定性、让人联想到弱惯性波湍流的渐进频率富集以及以多边形涡旋簇的形式产生的慢流形，证实了实验观察。详细讨论了这个涡旋簇，我们证明它源于涡度场的波状分量的总和和合并。这些波分量的性质、它们在一般条件下被检测到的可能性以及涡旋星团在更长的时间尺度上的最终命运仍有待探索。