The spherical Couette system, consisting of a viscous fluid between two differentially rotating concentric spheres, is studied using numerical simulations and compared with experiments performed at BTU Cottbus-Senftenberg, Germany. We concentrate on the case where the outer boundary rotates fast enough for the Coriolis force to play an important role in the force balance, and the inner boundary rotates slower or in the opposite direction as compared to the outer boundary. As the magnitude of differential rotation is increased, the system is found to transition through three distinct hydrodynamic regimes. The first regime consists of the emergence of the first non-axisymmetric instability. Thereafter one finds the onset of ‘fast’ equatorially antisymmetric inertial modes, with pairs of inertial modes forming triadic resonances with the first instability. A further increase in the magnitude of differential rotation leads to the flow transitioning to turbulence. Using an artificial excitation, we study how the background flow modifies the inertial mode frequency and structure, thereby causing departures from the eigenmodes of a full sphere and a spherical shell. We investigate triadic resonances of pairs of inertial modes with the fundamental instability. We explore possible onset mechanisms through numerical experiments.

The observation of global acoustic waves (p modes) in the Sun has been key to unveiling its internal structure and dynamics. A different kind of wave, known as sectoral Rossby modes, has been observed and identified, which potentially opens the door to probing internal processes that are inaccessible through p-mode helioseismology. Yet another set of waves, appearing as retrograde-propagating, equatorially antisymmetric vorticity waves, has also been observed but their identification remained elusive. Here, through a numerical model implemented as an eigenvalue problem, we provide evidence supporting the identification of those waves as a class of inertial eigenmodes, distinct from the Rossby-mode class, with radial velocities comparable to the horizontal ones deep in the convective zone but still small compared to the horizontal velocities toward the surface. We also suggest that the signature of tesseral-like Rossby modes might be present in recent observational data.

The formation and evolution of our solar system remains an outstanding question in planetary science (see Helled and Morbidelli (2021) for a review). Clues to these processes, however, remain in the form of the present day interiors of our planets (Helled et al., 2022). Variations on planetary formation pathways such as core accretion (Pollack et al., 1996), pebble accretion (Johansen & Lambrechts, 2017), or disk instability; early solar system conditions, and formation location will affect many physical properties such as the planet's heavy element

The magnetic field of the Earth yields clues to the dynamics of the present-day core dynamo and its history through magnetization in the crust (cf. Aubert et al., 2010). The internally generated magnetic field of the Earth arises predominantly from the dynamo in the outer core, and the structure and intensity of the field above the core is given by a potential field extrapolated from the core-mantle boundary ∼3,000 km below the surface (cf. Roberts & King, 2013). The dynamo field typically varies by ∼1% per decade and includes wave-like features at middle-to-low latitudes extending and propagating in longitude (cf. Finlay, Dumberry, et al., 2010). Sub-annual variations have also been observed and identified as geomagnetic jerks that exhibit rapid changes in the first and second time derivatives in the secular variation at a fixed observatory (Brown et al., 2013;Finlay et al., 2016;Mandea et al., 2010). While the mantle is not a dominant source of magnetic field, induction of currents in the mantle on time scales of hours to days in response to correspondingly