The non-linear fate of the elliptical instability in planetary cores - a local approach

Credits: NASA JPL Caltech, Europa

The growth of the oscillatory motion cannot last indefinitely, but what makes it stop has remained poorly understood. To determine what happens once the growth saturate, we use a local model of a liquid core. Instead of modeling the whole liquid core, we focus on a small fluid parcel. This is at far low numerical cost compared to a complete simulation of the core because the interaction of the fluid with deformed boundaries is arduous to achieve.

The use of the local model proves particularly efficient to probe the complex motions emerging from the saturation of the instability. If we let the flow freely evolve, we see the spontanous emergence of large vortices taking over the flow and killing the growing waves. But those eddies should feel wall friction because they are infinite in the direction along the rotation axis and connect to the boundaries of the core. If we take into account this specific wall friction, we observe an entirely different picture with smaller scale motion.

In the case of the saturation including wall friction, we have proven that the fluid motion inside the liquid core is a superposition of a multitude of oscillatory motion. This picture is truely similar to the undulating motion of the ocean's surface composed of many waves with quite different wavelength.

This work has led to a paper in Physical Review Letters. It has also been featured in Pour la Science.

In the study presented above, we assumed the fluid has an homogeneous density. We also investigated what happens when the core is stably stratified, i.e. when the core is denser at its base than at its top. We have proven that a similar instability takes place with the growth of oscillating and wavy patterns (called "internal waves") that breakdown into a swarm of new internal waves, similarly to what we have described above. This work has been published in Journal of Fluid Mechanics.

Useful links

• A NASA website summing up what is known about the interiors of terrestrial planets in the solar system