Instability of Tachocline Differential Rotation in a Shallow-Water Model, and the Solar Dynamo

Details Instability of Tachocline Differential Rotation in a Shallow-Water Model, and the Solar Dynamo Instability of Tachocline Differential Rotation in a Shallow-Water Model, and the Solar Dynamo

May 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000spd....31.0115d&link_type=abstract

American Astronomical Society, SPD Meeting #31, #01.15; Bulletin of the American Astronomical Society, Vol. 32, p.803

Astronomy and Astrophysics

Astronomy

Scientific paper

We examine the global, hydrodynamic stability of solar latitudinal differential rotation in a "shallow-water" model of the tachocline. Charbonneau, Dikpati and Gilman (1999, ApJ 526, 523) have recently shown that 2D disturbances are stable in the tachocline. In our model, the upper boundary of the thin shell is allowed to deform in latitude, longitude and time, thus including simplified 3D effects. We examine the stability of differential rotation as a function of the effective gravity of the stratification in the tachocline. High effective gravity corresponds to the radiative part of the tachocline; for this case, the instability is similar to the strictly 2D case. For low effective gravity, which corresponds to the overshoot part of the tachocline, a second mode of instability occurs, fed primarily by potential energy stored in the deformed shell. In this case, instability occurs for differential rotation down to about 13% between equator and pole. If this mode occurs in the Sun, it should destabilize much of the tachocline, even without a toroidal field. For the full range of effective gravity, the vorticity associated with the perturbations, coupled with radial motion due to horizontal divergence/convergence of the fluid, gives rise to a longitude-averaged, net kinetic helicity pattern, and hence a source of α -effect in the tachocline. Thus there could be a dynamo in the tachocline, driven by this α -effect and the latitudinal and radial gradients of rotation. Preliminary simulations suggest that an α -ω dynamo with the above α -effect working in the tachocline is capable of producing a reasonable butterfly diagram, particularly when a meridional circulation is included in the convective envelope, as is known to exist. Acknowledgement. This work has been partially supported by the NASA grant S-10145-X. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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