task 3: The fluid dynamics of core rotation

State-of-the-art and objectives: The convective dynamo model has proven successful to explain the Earth’s dynamo, and since its formulation, it has been applied to other planetary cores. However, its results are sometimes difficult to reconcile with available observational data, and its validity can be questioned in several configurations. For instance, the small size of the Moon and Ganymede makes it difficult to maintain a sufficient temperature gradient to sustain convection and to explain their past and present magnetic field, respectively (Dwyer et al. 2011, Le Bars et al. 2011, Sarson et al. 1997). Besides, the unusually low amplitude of the magnetic field on Mercury is difficult to explain with the standard scaling laws derived from convective models (e.g. Stanley et al. 2005). The energy budget of the early Earth is also difficult to reconcile with a convective dynamo before the onset of inner core growth (see e.g. Olson 2007). More generally, and even in planets where convection is present, it is of fundamental importance to also explore the role that other instabilities play in the organization of core flows.

A huge amount of energy is stored in the rotational motion of planets (spin and orbit), and one could thus rely on this reservoir to sustain intense flows. For instance, the rotational energy of the Earth-Moon system is approximately 1.7×10²⁹J, while the power necessary to sustain the present-day magnetic field of Earth is approximately 10¹¹W. Hence, less than 8% of the available rotation energy is necessary to sustain the dynamo over the age of Earth. The question is, How can the system extract energy from its rotation to drive intense fluid flows? If planets and stars were perfectly non-deformable systems rotating with a perfectly constant rotation vector, their fluid layers would behave rigidly and rotate as solid bodies. This is never the case. The rotation of a real celestial body is always perturbed by gravitational interactions with its companions, which generate periodic perturbations of its shape (i.e. tides), of the direction of its rotational vector (i.e. precession), and of its rotation rate (i.e. libration and length-of-day variation). Those three types of perturbations are generically called harmonic or mechanical forcings. Malkus (1963, 1968, 1989) was the first to highlight the relevance of those harmonic forcings for planetary core flows, but his work was at that time largely rejected, owing to a misunderstanding on the associated energy balances, as later elucidated by Kerswell (1996). The key point here is that small mechanical forcings do not provide the energy to drive the flows: they play the role of conveyers that extract part of the available rotational energy and convert it into intense fluid motions, generated by resonances and non-linear interactions of inertial modes sustained by rotation. Since this re-establishment, the fluid dynamics driven by mechanical forcing have been the subject of a growing interest in the fluid dynamics and planetary sciences communities, combining analytical, experimental and numerical studies (e.g. Busse 2010, Noir et al. 2001, Tilgner 2005, Zhang et al. 2011). We have significantly participated to this competitive, interdisciplinary, and multi-method research (e.g. Le Bars et al. 2015b). Schematically, one can today claim that the mechanisms and thresholds of flow instabilities driven by mechanical forcings are well known. In particular, one of the prevalent mechanism is the so-called elliptic instability, i.e. the parametric resonance of two inertial modes of the rotating flow with the elliptical base flow excited by either the tidal, the libration or the precession forcing in an ellipsoidal container (i.e. the generic form of a real planetary core). Previous studies have also demonstrated the relevance of mechanically forced flows at the planetary scales. For instance, precession (Dwyer et al. 2011), tides and libration (Le Bars et al. 2011) are now accepted as relevant “alternative” scenario for explaining the past Moon magnetic field. But at least three very challenging points remain to be tackled to validate those mechanically driven flows for planetary applications. First, the saturation process of the excited elliptical instability remains unknown, giving rise either to large cycles of growth, saturation and collapse, or to sustained bulk-filling turbulence (see e.g. Grannan et al. 2014). Then, the statistics of the excited turbulence remain out of reach of previous experimental and numerical studies, while their knowledge is necessary to understand the energy repartition between the various time and length scales: is this mechanically forced turbulence of rotating turbulence type, of Kolmogorov turbulence type, of wave turbulence type? Finally, the dynamo efficiency of such flows, as well as the typical amplitude and shape of the excited field, are still largely unknown. Breaking those three scientific challenges, using libration as a generic example of mechanically-driven flows, will be the subject of task 3 of the present project, combining innovative experiments and numerics.

Ongoing research projects:

• The non-linear fate of the elliptical instability in planetary cores - a local approach: T. Le Reun, B. Favier and M. Le Bars.
• The non-linear fate of the elliptical instability: experiments: T. Le Reun, B. Favier and M. Le Bars
• MHD simulations of the libration driven elliptical instability: S. R. Kanuganti, B. Favier and M. Le Bars.
• Dynamos generated by wave turbulence and mechanical forcing: M. Menu, F. Marcotte, B. Favier and M. Le Bars.

Open positions for this project: check out projects listed here