The predominant force balance in rapidly rotating planetary cores is between Coriolis, pressure, buoyancy and Lorentz forces. This magnetostrophic balance leads to a Taylor state where the spatially averaged azimuthal Lorentz force is compelled to vanish on cylinders aligned with the rotation axis. Any deviation from this state leads to a torsional oscillation, signatures of which have been observed in the Earth's secular variation and are thought to influence length of day variations via angular momentum conservation. In order to investigate the dynamics of torsional oscillations, we perform several three-dimensional dynamo simulations in a spherical shell. We find torsional oscillations, identified by their propagation at the correct Alfvén speed, in many of our simulations. We find that the frequency, location and direction of propagation of the waves are influenced by the choice of parameters. Torsional waves are observed within the tangent cylinder and also have the ability to pass through it. Several of our simulations display waves with core travel times of 4 to 6 years. We calculate the driving terms for these waves and find that both the Reynolds force and ageostrophic convection acting through the Lorentz force are important in driving torsional oscillations.
The westward drift component of the secular variation is likely to be a signal of waves riding on a background mean flow. By separating the wave and mean flow contributions, we can infer the strength of the “hidden” azimuthal part of the magnetic field within the core. We explore the origin of the westward drift commonly seen in dynamo simulations and show that it propagates at the speed of the slow magnetic Rossby waves with respect to a mean zonal flow. Our results indicate that such waves could be excited in the Earth's core and that wave propagation may indeed play some role in the longitudinal drift, particularly at higher latitudes where the wave component is relatively strong, the equatorial westward drift being dominated by the mean flow. We discuss a potential inference of the RMS toroidal field strength within the Earth's core from the observed drift rate.
Evidence for torsional oscillations (TOs) operating within the Earth's fluid outer core has been found in the secular variation of the geomagnetic field. These waves arise via disturbances to the predominant (magnetostrophic) force balance believed to exist in the core. The coupling of the core and mantle allow TOs to affect the length-of-day of the Earth via angular momentum conservation. Encouraged by previous work, where we were able to observe TOs in geodynamo simulations, we perform 3-D magnetoconvection simulations in a spherical shell in order to reach more Earth-like parameter regimes that proved hitherto elusive. At large Ekman numbers we find that TOs can be present but are typically only a small fraction of the overall dynamics and are often driven by Reynolds forcing at various locations throughout the domain. However, as the Ekman number is reduced to more Earth-like values, TOs become more apparent and can make up the dominant portion of the short timescale flow. This coincides with a transition to regimes where excitation is found only at the tangent cylinder, is delivered by the Lorentz force and gives rise to a periodic Earth-like wave pattern, approximately operating on a 4 to 5 year timescale. The core travel times of our waves also become independent of rotation at low Ekman number with many converging to Earth-like values of around 4 years.
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