Numerical Method for the Structure of Rotating Axisymmetric Stars and its Thermally Driven Circulation

我们计算了自引力和静止旋转环在粘性敲击下的平衡模型。我们选择了两种转动定律：线速度常数情形和比角动量常数情形。对于热源，我们模拟了由于粘性产生的热：Epsilon=nur^2(d omega/dr)^2，其中nu是运动粘性，其值是不确定的，所以我们将其作为一个参数。因此，对流运动在中心环状区被激发。然而，对于粘性源模型，主要结构取决于自重和离心力之间的平衡。因此，由于结构本身是对流稳定的，因此主要产生于旋转轴附近区域的大能量必须通过经向环流传递。激发出的经向环流在赤道平面上对称，在上半经平面上呈顺时针方向流动。如果选择最内表面离旋转轴很近或运动粘性值较大的构型，辐射压力就变得很重要，出现环状对流区，由于经向环流传递角动量，角速度分布会发生变化。如果我们假设状态将稳定到不允许循环的静止状态，温度恒定面应该比压力恒定面更多地向内移动到旋转轴。因此，角速度分布满足条件(d omega/dz)&lt；0。由于这样的分布对Goldreich-Schubert不稳定性是不稳定的，位形将在正压态和斜压态之间振荡。

We have computed equilibrium models for self-gravitating and stationary rotating toroids with viscous beating. We have chosen two kinds of rotation laws: linear velocity constant case and specific angular momentum constant case. As for the heat source we mimic heat generation due to viscosity as follows: epsilon = nuR^2 (d OMEGA/dR)^2, where nu is the kinematic viscosity whose value is uncertain and so we treat as a parameter.When we choose ring source model, its beat generation is so large that the energy cannot be transferred by radiation diffusion. Thus convective motion is excited in the central toroidal region. However, for the viscous source models, the main structure is determined by the balance between the self-gravity and centrifugal force. Thus the large energy which is mainly generated in the region near the rotation axis must be transferred by the meridional circulation because the structure itself is convectively stable. The excited meridional circulation is symmetric about the equatorial plane and its flow is clock wise direction in the upper half meridional plane. If we choose configuration whose innermost surface is very near the rotation axis or the value of kinematic viscosity to be large, the radiation pressure becomes important and toroidal convective region appears.Since the meridional circulation transfer the angular momentum, the angular velocity distribution will be changed. If we suppose that the state will settle down to a stationary state in which no circulation is allowed, the temperature constant surfaces should be shifted inward to the rotation axis much more than the pressure constant surfaces. Therefore the angular velocity distribution comes to satisfy the condition (d OMEGA/dz) < 0. Since such a distribution is unstable to Goldreich-Schubert instability, configuration will be oscillating between barotropic state and baroclinic state.