Polar waves and chaotic flows in thin rotating spherical shells

TL;DR

This paper investigates polar waves and chaotic flows in thin rotating spherical shells, revealing new symmetric and asymmetric rotating waves and their stability, with implications for understanding planetary atmospheres like Jupiter.

Contribution

It introduces novel symmetric and asymmetric polar rotating waves in thin spherical shells and analyzes their stability and chaotic behavior, advancing understanding of planetary atmospheric dynamics.

Findings

Discovery of stable symmetric and asymmetric polar rotating waves.

Identification of flow characteristics similar to planetary atmospheres.

Analysis of bifurcations leading to chaotic flows.

Abstract

Convection in rotating spherical geometries is an important physical process in planetary and stellar systems. Using continuation methods at low Prandtl number, we find both strong equatorially asymmetric and symmetric polar nonlinear rotating waves in a model of thermal convection in thin rotating spherical shells with stress-free boundary conditions. For the symmetric waves convection is confined to high latitude in both hemispheres but is only restricted to one hemisphere close to the pole in the case of asymmetric waves. This is in contrast to what is previously known from studies in the field. These periodic flows, in which the pattern is rotating steadily in the azimuthal direction, develop a strong axisymmetric component very close to onset. Using stability analysis of periodic orbits the regions of stability are determined and the topology of the stable/unstable oscillatory flows bifurcated from the branches of rotating waves is described. By means of direct numerical simulations of these oscillatory chaotic flows, we show that these three-dimensional convective polar flows exhibit characteristics, such as force balance or mean physical properties, which are similar to flows occuring in planetary atmospheres. We show that these results may open a route to understanding unexplained features of gas giant atmospheres, in particular for the case of Jupiter. These include the observed equatorial asymmetry with a pronounced decrease at the equator (the so-called dimple), and the coherent vortices surrounding the poles recently observed by the Juno mission.