We present an investigation into the nonlinear evolution of the Goldreich-Schubert-Fricke (GSF) instability using axisymmetric and three-dimensional simulations near the equator of a differentially rotating radiation zone. This instability may provide an important contribution to angular momentum transport in stars and planets. We adopt a local Boussinesq Cartesian shearing box model, which represents a small patch of a differentially rotating stellar radiation zone. Complementary simulations are also performed with stress-free, impenetrable boundaries in the local radial direction. The linear and nonlinear evolution of the equatorial axisymmetric instability is formally equivalent to the salt fingering instability. This is no longer the case in 3D, but we find that the instability behaves nonlinearly in a similar way to salt fingering. Axisymmetric simulations -- and those in 3D with short dimensions along the local azimuthal direction -- quickly develop strong jets along the rotation axis, which inhibit the instability and lead to predator-prey-like temporal dynamics. In 3D, the instability initially produces homogeneous turbulence and enhanced momentum transport, though in some cases jets form on a much longer timescale. We propose and validate numerically a simple theory for nonlinear saturation of the GSF instability and its resulting angular momentum transport. This theory is straightforward to implement in stellar evolution codes incorporating rotation. We estimate that the GSF instability could contribute towards explaining the missing angular momentum transport required in red giant stars, and play a role in the long-term evolution of the solar tachocline.
Thermal instabilities in accretion disks II: Numerical Experiments for the Goldreich-Schubert-Fricke Instability and the Convective Overstability in disks around young stars
本文通过数值实验验证了吸积盘中 GSF 与 COS 两种热不稳定性的理论增长率，发现 GSF 增长更快但近中平面停止，COS 最终主导，并揭示了观测所需分辨率要求。
Thermal baroclinic instabilities in accretion disks I: Combined dispersion relation for Goldreich-Schubert-Fricke Instability and Convective Overstability in disks around young stars
本文研究了年轻恒星周围盘中的热斜压不稳定性，推导了 GSF 和 COS 的组合色散关系并确定了新稳定性判据，发现斜压盘大气始终存在浮力不稳定方向，且长冷却时间下 GSF 模式会伴随相似增长率的 COS 模式。
Linear and nonlinear properties of the Goldreich-Schubert-Fricke instability in stellar interiors with arbitrary local radial and latitudinal differential rotation
Magnetohydrodynamic instabilities in stellar radiative regions. I. Linear study of shear-driven instabilities
Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎天文台，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）；Universitat Politècnica de Catalunya, BarcelonaTech (UPC)（加泰罗尼亚理工大学）；University of Leeds（利兹大学）；Northwestern University（西北大学）
Coexisting Tayler instability-driven dynamos in radiative zones: New dynamo solution and its impacts on stellar physics
Université de Genève（日内瓦大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；IRAP, Université de Toulouse, CNRS, CNES, UPS（图卢兹大学 IRAP 研究所）；Institut Universitaire de France (IUF)（法国高等研究院）
Effects of Magnetic Fields on Solar Inertial Modes in Global Nonlinear Simulations
Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）；Royal Observatory of Belgium（比利时皇家天文台）；High Altitude Observatory, NSF National Center for Atmospheric Research（美国国家科学基金会国家大气研究中心高海拔天文台）；National Center for Atmospheric Research（国家大气研究中心）
Nonlinear evolution of unstable solar inertial modes: The case of viscous modes on a differentially rotating sphere
Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系统研究所）；Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen（哥廷根大学天体物理与地球物理研究所）；Center for Astrophysics and Space Science, NYUAD Institute, New York University Abu Dhabi（纽约大学阿布扎比分校天体物理学与空间科学中心）；Department of Mechanical Engineering, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学机械工程系）
