Excitation of Inertial Modes in 3D Simulations of Rotating Convection in Planets and Stars

Thermal convection in rotating stars and planets drives anisotropic turbulence and differential rotation, both capable of feeding energy into global oscillations. Using 3D simulations of rotating convection in spherical shells, we show that inertial modes—oscillations restored by the Coriolis force—emerge naturally in rotationally constrained turbulence, without imposing any external forcing other than thermal/buoyancy driving. By varying the rotation rate at fixed Rayleigh number, we find that coherent modes appear only when the convective Rossby number, the ratio of the rotation period to the convective turnover time, falls below about one-half, where rotation dominates the dynamics. These modes are mostly retrograde in the rotating frame, equatorially symmetric, and confined to mid and high latitudes, with discrete frequencies well below twice the background rotation rate. At lower viscosities, or a smaller Prandtl number, mode excitation becomes more efficient and a broader spectrum of inertial modes emerges. While the precise excitation mechanism remains uncertain, our results suggest that the modes are driven by instabilities due to differential rotation rather than stochastic forcing by convection. We conclude that similar inertial modes are likely to exist in the interiors of giant planets and stars, though their low frequencies will make them difficult to detect.