Fluid Mechanics of Planets and Stars by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030220747
Publisher: Springer International Publishing

Fig. 4.16Illustration of the destabilization of the equatorial boundary layer caused by librations. The color scale represents the radial velocity.

This figure is adapted from Sauret et al. (2013) Fig. 2

Conclusion—Beyond the Elliptical Instability in Planetary Cores

In this chapter, we have presented how gravitational interactions are able to create complex, and even turbulent flows, inside planetary cores. We have particularly focused on a specific class of instability related to parametric sub-harmonic resonance, drawing an analogy between rotating fluid cavities and a length-varying pendulum. Such a resonance, also called “elliptical instability”, builds on the coupling between two inertial waves and the oscillating strain field induced by tidal interactions. Despite recent advances that have been presented above, many challenges remain to describe the turbulent saturation flows and the induced magnetic field. Also, while tides distortion, libration, precession, and convection have up to now been mainly studied separately, they might be simultaneously present in planetary cores, possibly leading to complex nonlinear interactions that remain to be explored.

A concluding remark: parametric resonance is not the only class of instabilities that can be driven by tides inside planetary cores. For instance, libration leads to centrifugal instability of the equatorial boundary layer (Calkins et al. 2010; Favier et al. 2014). As shown numerically by Sauret et al. (2013), this excited motion in the boundary layer radiates inertial waves in the whole interior—see Fig. 4.16. Lastly, the excitation of inertial modes inside a fluid cavity drives, via interactions with and within the boundary layer, zonal winds, i.e. axisymmetric geostrophic flows, associated with intense shear that may be unstable (Sauret et al. 2010, 2014). All these different excited flows pile up in planetary cores and their respective contributions remain to be evaluated. In any case, we hope to have convinced the reader that tidal interactions lead to complexity in the behavior of fluid interiors, and should not be dismissed for being “small” perturbations.

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