Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the ax...

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Bibliographic Details
Published in:The Astrophysical journal 2024-05, Vol.966 (2), p.195
Main Authors: Tripathi, B., Barker, A. J., Fraser, A. E., Terry, P. W., Zweibel, E. G.
Format: Article
Language:English
Subjects:
Angular momentum
Approximation
Astrophysical fluid dynamics
Closure approximation
Differential rotation
Diffusion rate
Direct numerical simulation
Extrasolar gaseous giant planets
Hydrodynamics
Instability
Mathematical models
Momentum
Numerical simulations
Parameters
Planetary rotation
Rotation
Solar differential rotation
Stability
Stellar interiors
Stellar rotation
Thermal diffusion
Turbulence
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Summary:Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.
ISSN:0004-637X
1538-4357
DOI:10.3847/1538-4357/ad38c3