Detailed observations of the velocities of Jovian vortices exist at only one height in the atmosphere, so their vertical structures are poorly understood. This motivates this study that computes stable three-dimensional, long-lived planetary vortices that satisfy the equations of motion. We solve the anelastic equations with a high-resolution pseudo-spectral method using the observed Jovian atmospheric temperatures and zonal flow. We examine several families of vortices and find that constant-vorticity vortices, which have nearly uniform vorticity as a function of height, and horizontal areas that go to zero at their tops and bottoms, converge to stable vortices that look like the Great Red Spot (GRS) and other Jovian anticyclones. In contrast, the constant-area vortices proposed in previous studies, which have nearly uniform areas as a function of height, and vertical vorticities that go to zero at their tops and bottoms, are far from equilibrium, break apart, and converge to constant-vorticity vortices. Our late-time vortices show unexpected properties. Vortices that are initially non-hollow become hollow (i.e. have local minima of vertical vorticity at their centres), which is a feature of the GRS that cannot be explained with two-dimensional simulations. The central axes of the final vortices align with the planetary spin axis even if they align initially with the local direction of gravity. We present scaling laws for how vortex properties change with the Rossby number and other non-dimensional parameters. We prove analytically that the horizontal mid-plane of a stable vortex must lie at a height above the top of the convective zone.

中文翻译：

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稳定的三维涡旋家族与包括大红斑在内的木星观测结果一致

对木星涡旋速度的详细观测仅存在于大气层的一个高度，因此人们对其垂直结构知之甚少。这激发了这项研究，计算满足运动方程的稳定的三维、长寿命的行星涡旋。我们利用观测到的木星大气温度和纬向流，通过高分辨率伪谱方法求解滞弹性方程。我们检查了几个涡流族，发现恒定涡度涡流具有几乎均匀的涡度作为高度的函数，以及在顶部和底部趋于零的水平面积，会聚成看起来像大红斑的稳定涡流（ GRS）和其他木星反气旋。相比之下，先前研究中提出的恒定面积涡旋，其面积随高度变化而几乎均匀，并且垂直涡旋在顶部和底部趋于零，远离平衡，分裂并收敛到恒定-涡度 涡流。我们的晚期漩涡表现出意想不到的特性。最初非空心的涡流会变成空心的（即在其中心具有垂直涡度的局部最小值），这是 GRS 的一个特征，无法用二维模拟来解释。最终漩涡的中心轴与行星自转轴对齐，即使它们最初与局部重力方向对齐。我们提出了涡旋属性如何随罗斯比数和其他无量纲参数变化的比例定律。我们通过分析证明，稳定涡旋的水平中面必须位于对流区顶部上方的高度。