Baroclinic instability in the solar tachocline

The solar tachocline is likely to be close to a geostrophic "thermal wind," for which the Coriolis force associated with differential rotation is closely balanced by a latitudinal pressure gradient, leading to a tight relation between the vertical gradient of rotation and the latitudinal entropy gradient. Using a hydrostatic but nongeostrophic spherical shell model, we examine baroclinic instability of the tachocline thermal wind. We find that both the overshoot and radiative parts of the tachocline should be baroclinicly unstable at most latitudes. Growth rates are roughly five times higher in middle and high latitudes compared to low latitudes, and much higher in the overshoot than in the radiative tachocline. They range in e-folding amplification from 10 days in the high latitude overshoot tachocline, down to 20 yr for the low latitude radiative tachocline. In the radiative tachocline only, longitudinal wavenumbers m = 1, 2 are unstable, while in the overshoot tachocline a much broader range of m are unstable. At all latitudes and with all stratifications, the longitudinal scale of the most unstable mode is comparable to the Rossby deformation radius, while the growth rate is set by the local latitudinal entropy gradient. Baroclinic instability in the tachocline competing with instability of the latitude rotation gradient established in earlier studies should be important for the workings of the solar dynamo and should be expected to be found in most stars that contain an interface between radiative and convective domains.