4.3 Buoyancy breakup of a shear-generated magnetic layer

UpdateJump To The Next Update Information Instead of prescribing an unstable equilibrium of an initial magnetic flux tube or layer, Vasil and Brummell (2008Jump To The Next Citation Point) carried out a series of 3D MHD simulations of the generation of a strong layer of horizontal magnetic field by the action of a vertical shear on a weak vertical field in a subadiabatically stratified atmosphere, and examine the subsequent breakup of the resulting magnetic configuration via magnetic buoyancy instabilities (see Figure 11View Image).
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Figure 11: From Vasil and Brummell (2008Jump To The Next Citation Point). A 3D MHD simulation of the build up and subsequent buoyancy break up of a layer of horizontal magnetic field forced by a vertical shear on an initially weak vertical field in a subadiabatically stratified atmosphere. The sequence of images show the volume renderings of the magnetic field strength. Figure reproduced by permission of the AAS.

The aim of these simulations is to examine under what conditions the radial shear of differential rotation operating in the thin solar tachocline layer can amplify a strong enough large scale toroidal magnetic field that undergoes magnetic buoyancy instabilities and develops buoyantly rising structures. The numerical simulations together with a subsequent analytical study (Vasil and Brummell, 2009Jump To The Next Citation Point) show that magnetic buoyancy instabilities can indeed develop in the shear-generated magnetic layer (Figure 11View Image) if the forcing that drives the shear flow is sufficiently large. The needed forcing is such that, in the absence of the magnetic field, it imposes a hydrodynamically unstable shear. It is found that the imposed shear needs to have a Richardson number Ri being less than 1, where Ri measures the relative importance of the stabilizing effect of the stratification over the strength of the shear to overturn the fluid (Vasil and Brummell, 2009Jump To The Next Citation PointSilvers et al., 2009Jump To The Next Citation Point). This result is not surprising because in order for the magnetic layer to be buoyantly unstable, the imposed shear flow needs to transfer enough energy to the magnetic field for it to overcome the stable background stratification (Silvers et al., 2009Jump To The Next Citation Point). It is not clear whether such strong forcing of the shear exists in the solar tachocline. For the observed shear in the solar tachocline, the Richardson number is estimated to be much greater than 1, 3 5 Ri ∼ 10 – 10 (Gough, 2007). However, the observed shear in the tachocline may not correspond to the forcing shear, but is the end steady-state reached when the forcing is balanced by the built-up magnetic stress and turbulent transport.

Silvers et al. (2009Jump To The Next Citation Point) further extend the studies of Vasil and Brummell (2008) and Vasil and Brummell (2009) by considering the fact that the ratio of the magnetic diffusivity (η) over the thermal diffusivity (κ) in the solar tachocline is very small: ξ = η∕κ ≪ 1. Under such conditions the double-diffusive magnetic buoyancy instabilities can develop at a much less steep magnetic pressure gradient for the magnetic layer compared to that required for magnetic buoyancy instabilities under the assumption of adiabatic evolution (see end of Section 4.2). The stabilizing effect of the subadiabatic stratification is significantly reduced by the thermal diffusion. Simulations by Silvers et al. (2009) verify that double-diffusive magnetic buoyancy instabilities indeed can develop for a magnetic layer generated by a weak forcing shear that is hydrodynamically stable (with Ri > 2.96).


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