Two-dimensional hydrodynamic calculations of the nonlinear development of the Goldreich-Schubert-Fricke instability in a rotating annulus

Details Two-dimensional hydrodynamic calculations of the nonlinear development of the Goldreich-Schubert-Fricke instability in a rotating annulus Two-dimensional hydrodynamic calculations of the nonlinear development of the Goldreich-Schubert-Fricke instability in a rotating annulus

Nov 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991apj...381..515k&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 381, Nov. 10, 1991, p. 515-525.

Statistics

Computation

10

Computational Astrophysics, Hydrodynamics, Planetary Rotation, Stellar Rotation, Systems Stability, Angular Momentum, Annuli, Gas Giant Planets, Nonlinear Systems, Rotating Matter

Scientific paper

Two-dimensional nonlinear hydrodynamic calculations are presented which may help assess the effectiveness of the instability in transporting angular momentum in the equatorial zones of stars and planets which are stably stratified with respect to convection. The calculations were made by numerically integrating the 2D axisymmetric Navier-Stokes equations, including viscosity and heat conduction. The instability was followed into the nonlinear regime. The maximum rms velocity amplitude was found to correlate well with the product of the linear growth rate and radial length scale of the instability, consistent with the idea that the instability grows to an amplitude such that an eddy turnover time becomes equal to the growth time defined by the inverse of the growth rate. The time scale for angular momentum to be redistributed to a state of marginal stability was consistent with this picture. The results suggest that in physical situations a state of marginal stability will be maintained, since departures from such a state will be rapidly corrected.

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