论文标题
改进了拉普拉斯潮汐方程特征值的渐近表达式
Improved Asymptotic Expressions for the Eigenvalues of Laplace's Tidal Equations
论文作者
论文摘要
Laplace的潮汐方程控制了在所谓的传统近似中处理均匀旋转时恒星中振荡的角度依赖性。使用扰动扩展方法，我得出了与这些方程相关的特征值的改进表达式，在大型自旋参数$ q $的渐近极限中有效。这些表达式具有订单$ q^{ - 3} $的相对精度，用于授权惯性模式，而Rossby和Kelvin模式的$ q^{ - 1} $;对于所有三种模式类型，相应的绝对精度是$ q^{ - 1} $的顺序。我根据数值计算来验证分析，并证明如何将其应用于Rossby模式的时期和本征函数的推导公式。
Laplace's tidal equations govern the angular dependence of oscillations in stars when uniform rotation is treated within the so-called traditional approximation. Using a perturbation expansion approach, I derive improved expressions for the eigenvalue associated with these equations, valid in the asymptotic limit of large spin parameter $q$. These expressions have a relative accuracy of order $q^{-3}$ for gravito-inertial modes, and $q^{-1}$ for Rossby and Kelvin modes; the corresponding absolute accuracy is of order $q^{-1}$ for all three mode types. I validate my analysis against numerical calculations, and demonstrate how it can be applied to derive formulae for the periods and eigenfunctions of Rossby modes.
