Angular momentum transport by the GSF instability: nonlinear simulations at the equator. (arXiv:1905.06962v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Barker_A/0/1/0/all/0/1">Adrian J. Barker</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Jones_C/0/1/0/all/0/1">Chris A. Jones</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tobias_S/0/1/0/all/0/1">Steven M. Tobias</a>
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.
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.
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