Angular momentum transport, layering, and zonal jet formation by the GSF instability: non-linear simulations at a general latitude

Abstract

We continue our investigation into the non-linear evolution of the Goldreich–Schubert–Fricke (GSF) instability in differentially rotating radiation zones. This instability may be a key player in transporting angular momentum in stars and giant planets, but its non-linear evolution remains mostly unexplored. In a previous paper we considered the equatorial instability, whereas here we simulate the instability at a general latitude for the first time. We adopt a local Cartesian Boussinesq model in a modified shearing box for most of our simulations, but we also perform some simulations with stress-free, impenetrable, radial boundaries. We first revisit the linear instability and derive some new results, before studying its non-linear evolution. The instability is found to behave very differently compared with its behaviour at the equator. In particular, here we observe the development of strong zonal jets (‘layering’ in the angular momentum), which can considerably enhance angular momentum transport, particularly in axisymmetric simulations. The jets are, in general, tilted with respect to the local gravity by an angle that corresponds initially with that of the linear modes, but which evolves with time and depends on the strength of the flow. The instability transports angular momentum much more efficiently (by several orders of magnitude) than it does at the equator, and we estimate that the GSF instability could contribute to the missing angular momentum transport required in both red giant and subgiant stars. It could also play a role in the long-term evolution of the solar tachocline and the atmospheric dynamics of hot Jupiters.

Horizontal shear instabilities in rotating stellar radiation zones

“…These mechanisms have not been identified yet even if several candidates have been proposed, such as stable and unstable magnetic fields (e.g., Moss 1992;Charbonneau & MacGregor 1993;Spruit 1999Spruit , 2002Fuller et al 2019), stochastically-excited internal gravity waves (e.g., Talon & Charbonnel 2005;Rogers 2015; Pinçon et al 2017), and mixed gravito-acoustic modes (Belkacem et al 2015a,b). In this framework, improving our knowledge of the hydrodynamical turbulent transport induced by the instabilities of the stellar differential rotation is mandatory since it has been recently proposed as another potential efficient mechanism to transport angular momentum (Barker et al 2020;Garaud 2020) while it constitutes one of the cornerstones of the theory of the rotational transport and mixing along the evolution of stars (Zahn 1992).…”

Numerical study of the McIntyre instability around Gaussian floating vortices in thermal wind balance

“…Combining salt stratification and thermal effects (by heating the ellipsoid) would allow to also explore the competition with the double diffusive instability, as relevant for meddies. From the numerical point of view, it is obviously necessary now to explore three-dimensional and turbulent flows, accounting both for the small Ekman number of real meddies and for their chaotic environment: this is already done in astrophysics in the Sc 1 limit [26], which actually could also be relevant for oceanic applications (see section V). Beyond this computational challenge, it would already be interesting, with the present basic numerical tool, to study the non-linear, longterm evolution of the instability in order to quantify its saturation state and its mixing efficiency.…”

Modeling coexisting GSF and shear instabilities in rotating stars

“…where we note that the fastest-growing modes can take a larger or smaller value than 𝑑 depending on the parameters (see e.g. the Appendix of Barker et al 2020). The unstable region of parameter space can be written as…”

“…There are many possible sources of extra mixing in stars, as discussed for instance by Zahn (1974). Of particular interest in recent years are the diffusive (alternatively called secular) shear instability (Zahn 1974(Zahn , 1992Prat & Lignières 2013;Prat & Lignières 2014;Garaud et al 2015;Garaud & Kulenthirarajah 2016;Prat et al 2016;Garaud et al 2017;Gagnier & Garaud 2018), and the Goldreich-Schubert-Fricke (GSF) instability (Goldreich & Schubert 1967;Fricke 1968;Knobloch & Spruit 1982;Knobloch 1982;Korycansky 1991;Rashid et al 2008;Barker et al 2019Barker et al , 2020, that can extract energy from the differential rotation of the star to drive turbulence, and therefore transport of chemical species and angular momentum. In what follows, we begin by briefly reviewing what is known about both types of instabilities and their transport properties, and then discuss what outstanding issues remain to be studied.…”

“…We ignore magnetic fields, for simplicity, but acknowledge that they would in practice form an important part of the complete story. Again for simplicity, we consider only ★ E-mail: eonhochang@math.arizona.edu; pgaraud@ucsc.edu the equatorial region of a star, noting that the non-equatorial case is substantially more complicated (Knobloch & Spruit 1982;Barker et al 2020). Near the equator, by symmetry, the angular velocity Ω is a function of the radius 𝑟 only, so that we can assume that Ω = Ω(𝑟).…”