截头椭圆锥中的惯性波超吸引子
Inertial wave super-attractor in a truncated elliptical cone
AI总结：
研究非轴对称三维旋转腔体中截头椭圆锥内的惯性波传播，通过射线追踪、渐近分析和数值模拟，发现破坏轴对称性可使吸引子被困于三维特定平面内，且所有射线均收敛于流体内部的同一极限环。
摘要：
我们考虑在包含于非轴对称三维旋转腔体中的流体中传播的惯性波。我们关注流体被封闭在截头锥或平截头体内部的特定情况，该体积位于切割直立圆锥的两个水平平行平面之间。虽然这种几何形状过去曾被研究过，但我们通过破坏其轴对称性对其进行推广，并考虑水平截面为椭圆而非圆形的截头椭圆锥情况。该问题首先通过射线追踪解决，其中局部波包在闭合体积内进行几何传播和反射且无衰减。我们用局部渐近分析和原始线性黏性问题的数值模拟补充了这些结果。我们表明，在二维或轴对称域中众所周知的吸引子，只要破坏域的轴对称性，就可以在三维中被困在特定平面内。与三维域中吸引子的先前例子相反，所有射线都收敛到相同的极限环，而不管初始条件如何，并且它位于流体内部。
英文摘要：
We consider inertial waves propagating in a fluid contained in a non-axisymmetric three-dimensional rotating cavity. We focus on the particular case of a fluid enclosed inside a truncated cone or frustum, which is the volume that lies between two horizontal parallel planes cutting an upright cone. While this geometry has been studied in the past, we generalise it by breaking its axisymmetry and consider the case of a truncated elliptical cone for which the horizontal sections are elliptical instead of circular. The problem is first tackled using ray tracing where local wave packets are geometrically propagated and reflected within the closed volume without attenuation. We complement these results with a local asymptotic analysis and numerical simulations of the original linear viscous problem. We show that the attractors, well-known in two dimensional or axisymmetric domains, can be trapped in a particular plane in three-dimension provided that the axisymmetry of the domain is broken. Contrary to previous examples of attractors in three-dimensional domains, all rays converge towards the same limit cycle regardless of initial conditions, and it is localised in the bulk of the fluid.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
