论文标题
差异旋转球上的粘性惯性模式：与太阳观测的比较
Viscous inertial modes on a differentially rotating sphere: Comparison with solar observations
论文作者
论文摘要
在上一篇论文中，我们研究了纬度旋转对β平面近似中太阳赤道罗斯比模式的影响。从那时起，在太阳上观察到了丰富的惯性模式，该模式不仅限于赤道罗斯比模式，并包括高纬度模式。 在这里，我们使用逼真的太阳差旋转（包括粘性阻尼）将2D中环形模式的计算扩展到球形几何形状。目的是将计算模式光谱与观测值进行比较并研究模式稳定性。 在固定半径下，我们使用速度流函数的球形谐波分解来数字解决特征值问题。由于存在粘性临界层，该频谱由四个不同的家族组成：Rossby模式，高纬度模式，临界纬度模式和强烈阻尼模式。对于每个纵向波数M <4，与仅存在赤道rossby模式的赤道beta平面相比，球体上最多有三种类似Rossby的模式。模型中最少的阻尼模式具有类似于观察到的模式的本征频和本征函数。当半径在对流区的下半部分配时，比较会有所改善。对于高于0.75R和Ekman编号E <10^{ - 4}的半径，至少一种模式是不稳定的。对于M = 1或M = 2，当Ekman数字的径向依赖性遵循对流区基部的淬火扩散模型（E =2。10^{-5}）时，最多两个Rossby模式是不稳定的。对于M = 3，最多两种Rossby模式可能不稳定，包括赤道Rossby模式。 尽管此处讨论的2D模型是高度简化的，但环形模式的光谱似乎包括许多观察到的太阳惯性模式。该模型中的自启动模式的频率接近具有最大幅度的观察到的模式的频率。
In a previous paper we studied the effect of latitudinal rotation on solar equatorial Rossby modes in the beta-plane approximation. Since then, a rich spectrum of inertial modes has been observed on the Sun, which is not limited to the equatorial Rossby modes and includes high-latitude modes. Here we extend the computation of toroidal modes in 2D to spherical geometry, using realistic solar differential rotation and including viscous damping. The aim is to compare the computed mode spectra with the observations and to study mode stability. At fixed radius, we solve the eigenvalue problem numerically using a spherical harmonics decomposition of the velocity stream function. Due to the presence of viscous critical layers, the spectrum consists of four different families: Rossby modes, high-latitude modes, critical-latitude modes, and strongly damped modes. For each longitudinal wavenumber m<4, up to three Rossby-like modes are present on the sphere, in contrast to the equatorial beta plane where only the equatorial Rossby mode is present. The least damped modes in the model have eigenfrequencies and eigenfunctions that resemble the observed modes; the comparison improves when the radius is taken in the lower half of the convection zone. For radii above 0.75R and Ekman numbers E<10^{-4}, at least one mode is unstable. For either m=1 or m=2, up to two Rossby modes are unstable when the radial dependence of the Ekman number follows a quenched diffusivity model (E=2. 10^{-5} at the base of the convection zone). For m=3, up to two Rossby modes can be unstable, including the equatorial Rossby mode. Although the 2D model discussed here is highly simplified, the spectrum of toroidal modes appears to include many of the observed solar inertial modes. The self-excited modes in the model have frequencies close to those of the observed modes with the largest amplitudes.
