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

我们计算了具有粘性跳动的自重力和静止旋转环面的平衡模型。我们选择了两种旋转定律：线速度常数和比角动量常数。对于热源，我们模拟粘度产生的热量如下：epsilon = nuR^2 (d OMEGA/dR)^2，其中nu是运动粘度，其值是不确定的，因此我们将其作为参数。当我们选择环源模型时，其产生的热量很大，不能通过辐射扩散传递能量。因此，在中心环面区域激发对流运动。然而，对于粘性源模型，主要结构是由自重力和离心力之间的平衡决定的。因此，主要在旋转轴附近区域产生的大能量必须通过经向环流传递，因为结构本身是对流稳定的。受激经向环流在赤道面对称，在上半部经向面沿时钟方向流动。如果我们选择最内表面非常靠近旋转轴或运动粘度值较大的构型，则辐射压力变得重要，并出现环面对流区域。由于经向环流传递角动量，使得角速度分布发生变化。如果我们假设状态将稳定到不允许循环的稳态，则温度常数表面应该比压力常数表面更向内移动到旋转轴上。因此，角速度分布满足(d ω /dz) < 0的条件。由于这种分布对golddreich - schubert不稳定是不稳定的，构型将在正压状态和斜压状态之间振荡。

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.