We present an analytical model that unifies many of the inertial waves that have been recently observed on the surface of the Sun, as well as many other modes that have been theoretically predicted—but have yet to be observed—into a single family of mixed inertial modes. By mixed, we mean that the prograde- and retrograde-propagating members of this family have different restoring forces and hence different behavior. Thermal Rossby waves exist as prograde-propagating waves, while the high-frequency retrograde (HFR) wave is one example of a member of the retrograde branch. This family of mixed modes has fully 3D motions that satisfy the anelastic form of the continuity condition. As such, the horizontal velocity is both vortical and divergent with the later flow component associated with a dynamically important radial velocity. The modes are differentiated by the number of nodes in latitude, with the lowest latitudinal order corresponding to the traditional thermal Rossby wave of Busse, the first latitudinal overtone to the mixed mode of Bekki et al., and the second overtone to the HFR wave discovered by Hanson et al. There also exist infinitely more modes of higher latitudinal order whose frequencies increase as the order increases. These higher overtones may correspond to many of the inertial modes that have been recently identified by numerical eigenmode solvers.

中文翻译：

---

太阳混合惯性模式的统一模型

我们提出了一个分析模型，它将最近在太阳表面观察到的许多惯性波以及理论上预测但尚未观察到的许多其他模式统一为一个单一的波族混合惯性模式。通过混合，我们的意思是该家族的顺行和逆行传播成员具有不同的恢复力，因此具有不同的行为。热罗斯贝波以顺行波的形式存在，而高频逆行波 (HFR) 则是逆行波的一个例子。这一系列混合模式具有完全 3D 运动，满足连续性条件的滞弹性形式。因此，水平速度既是涡旋的又是发散的，而后面的流动分量与动态重要的径向速度相关。这些模式通过纬度上的节点数量来区分，最低纬度阶对应于 Busse 的传统热罗斯贝波，第一纬度泛音对应于 Bekki 等人的混合模式，第二泛音对应于发现的 HFR 波汉森等人。还存在无限多的高纬度阶模，其频率随着阶数的增加而增加。这些更高的泛音可能对应于最近由数值本征模式求解器识别的许多惯性模式。