A Unifying Model of Mixed Inertial Modes in the Sun

Abstract

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.