# Baroclinic Instability in the Solar Tachocline for Continuous Vertical Profiles of Rotation, Effective Gravity, and Toroidal Field

## Abstract

We present results from an MHD model for baroclinic instability in the solar tachocline that includes rotation, effective gravity, and toroidal field that vary continuously with height. We solve the perturbation equations using a shooting method. Without toroidal fields but with an effective gravity declining linearly from a maximum at the bottom to much smaller values at the top, we find instability at all latitudes except at the poles, at the equator, and where the vertical rotation gradient vanishes (32.°3) for longitude wavenumbers m from 1 to >10. High latitudes are much more unstable than low latitudes, but both have e -folding times that are much shorter than a sunspot cycle. The higher the m and the steeper the decline in effective gravity, the closer the unstable mode peak to the top boundary, where the energy available to drive instability is greatest. The effect of the toroidal field is always stabilizing, shrinking the latitude ranges of instability as the toroidal field is increased. The larger the toroidal field, the smaller the longitudinal wavenumber of the most unstable disturbance. All latitudes become stable for a toroidal field exceeding about 4 kG. The results imply that baroclinic instability should occur in themore »

- Authors:

- High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green, Boulder, CO 80307-3000 (United States)

- Publication Date:

- OSTI Identifier:
- 22663277

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 842; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DISTURBANCES; EQUATIONS; GRAVITATION; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PERTURBATION THEORY; ROTATION; SUN; SUNSPOTS

### Citation Formats

```
Gilman, Peter A., E-mail: gilman@ucar.edu.
```*Baroclinic Instability in the Solar Tachocline for Continuous Vertical Profiles of Rotation, Effective Gravity, and Toroidal Field*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA7682.

```
Gilman, Peter A., E-mail: gilman@ucar.edu.
```*Baroclinic Instability in the Solar Tachocline for Continuous Vertical Profiles of Rotation, Effective Gravity, and Toroidal Field*. United States. doi:10.3847/1538-4357/AA7682.

```
Gilman, Peter A., E-mail: gilman@ucar.edu. Tue .
"Baroclinic Instability in the Solar Tachocline for Continuous Vertical Profiles of Rotation, Effective Gravity, and Toroidal Field". United States.
doi:10.3847/1538-4357/AA7682.
```

```
@article{osti_22663277,
```

title = {Baroclinic Instability in the Solar Tachocline for Continuous Vertical Profiles of Rotation, Effective Gravity, and Toroidal Field},

author = {Gilman, Peter A., E-mail: gilman@ucar.edu},

abstractNote = {We present results from an MHD model for baroclinic instability in the solar tachocline that includes rotation, effective gravity, and toroidal field that vary continuously with height. We solve the perturbation equations using a shooting method. Without toroidal fields but with an effective gravity declining linearly from a maximum at the bottom to much smaller values at the top, we find instability at all latitudes except at the poles, at the equator, and where the vertical rotation gradient vanishes (32.°3) for longitude wavenumbers m from 1 to >10. High latitudes are much more unstable than low latitudes, but both have e -folding times that are much shorter than a sunspot cycle. The higher the m and the steeper the decline in effective gravity, the closer the unstable mode peak to the top boundary, where the energy available to drive instability is greatest. The effect of the toroidal field is always stabilizing, shrinking the latitude ranges of instability as the toroidal field is increased. The larger the toroidal field, the smaller the longitudinal wavenumber of the most unstable disturbance. All latitudes become stable for a toroidal field exceeding about 4 kG. The results imply that baroclinic instability should occur in the tachocline at latitudes where the toroidal field is weak or is changing sign, but not where the field is strong.},

doi = {10.3847/1538-4357/AA7682},

journal = {Astrophysical Journal},

number = 2,

volume = 842,

place = {United States},

year = {Tue Jun 20 00:00:00 EDT 2017},

month = {Tue Jun 20 00:00:00 EDT 2017}

}