Laboratory experiments and numerical simulations of inertial wave-interactions in a rotating spherical shell

Abstract

In homogeneous rotating fluids inertial waves can occur. These waves are an essential element for the motion in the liquid outer core of the Earth, the atmosphere and the oceans. We investigate such waves for the rotating spherical shell geometry. For this geometry, a theoretical understanding is hampered due to the occurrence of singularities and a complicated Ekman layer structure. In the experiment, the inner sphere's rotation is modulated in form of a sinus curve. The waves propagate in the fluid with a fixed angle respect to the rotation axis. The angle depends on the wave frequency. Due to multiple reflections at the spherical boundaries, wave energy can be focused on certain orbits. Preliminary results show the generation of higher harmonics in the equatorial region of the shell. We also find a vertical layer, touching the inner sphere's equator. The layer is reminiscent of a Stewartson layer but shows a different spatial structure. Finally, the laboratory experiment is compared with numerical simulations. Good agreement can be found.