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We present an investigation into the nonlinear evolution of theGoldreich-Schubert-Fricke (GSF) instability using axisymmetric andthree-dimensional simulations near the equator of a differentially rotatingradiation zone. This instability may provide an important contribution toangular momentum transport in stars and planets. We adopt a local BoussinesqCartesian shearing box model, which represents a small patch of adifferentially rotating stellar radiation zone. Complementary simulations arealso performed with stress-free, impenetrable boundaries in the local radialdirection. The linear and nonlinear evolution of the equatorial axisymmetricinstability is formally equivalent to the salt fingering instability. This isno longer the case in 3D, but we find that the instability behaves nonlinearlyin a similar way to salt fingering. Axisymmetric simulations -- and those in 3Dwith short dimensions along the local azimuthal direction -- quickly developstrong jets along the rotation axis, which inhibit the instability and lead topredator-prey-like temporal dynamics. In 3D, the instability initially produceshomogeneous turbulence and enhanced momentum transport, though in some casesjets form on a much longer timescale. We propose and validate numerically asimple theory for nonlinear saturation of the GSF instability and its resultingangular momentum transport. This theory is straightforward to implement instellar evolution codes incorporating rotation. We estimate that the GSFinstability could contribute towards explaining the missing angular momentumtransport required in red giant stars, and play a role in the long-termevolution of the solar tachocline.

Angular momentum transport by the GSF instability: nonlinear simulations at the equator