局部等温和多变盘中Rossby波不稳定性：三维线性计算
Rossby wave instability in locally isothermal and polytropic disks: three-dimensional linear calculations
摘要：
本文给出了全球三维盘中线性Rossby波不稳定性（RWI）的数值计算。线性化的流体方程求解垂直分层，径向结构的磁盘与局部等温或多方状态方程，通过分解成厄米和Gegenbauer多项式，分别扰动的水动力量的垂直依赖。经确认，RWI在3D中运行。对于上面假设的具有垂直依赖性的扰动，3D和二维（2D）计算之间的增长率几乎没有差异。这种类型的2D和3D解决方案之间的比较表明，RWI主要是一个2D的不稳定性和三维的影响，如垂直运动，被解释为一个扰动的结果占主导地位的2D流。研究了绕同向旋转的垂向流动，在这种情况下可能形成旋涡。在局部等温的圆盘中，预期的涡心保持近似垂直的流体静力平衡。对于多变盘，涡心具有正的垂直速度，其大小随多变指数$n$的减小而增大。
英文摘要：
Numerical calculations of the linear Rossby wave instability (RWI) in global three-dimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and two-dimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggest the RWI is predominantly a 2D instability and that three-dimensional effects, such as vertical motion, to be interpreted as a perturbative consequence of the dominant 2D flow. The vertical flow around co-rotation, where vortex-formation is expected, is examined. In locally isothermal disks the expected vortex center remains in approximate vertical hydrostatic equilibrium. For polytropic disks the vortex center has positive vertical velocity, whose magnitude increases with decreasing polytropic index $n$.
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