  We perform idealised numerical simulations of magnetic buoyancy instabilities
in a model of the solar tachocline. We introduce a simplified model of magnetic
flux pumping in an upper layer (the convection zone), and study the effects of
its inclusion on the evolution of buoyancy instabilities in a lower layer (the
radiative interior). We study its effects on the instability of both a
preconceived magnetic slab and of a shear-generated magnetic layer. In the
former, we find that in the regime in which the downward pumping velocity is
comparable with the Alfven speed of the magnetic layer, flux pumping is able to
hold back the bulk of the magnetic field, with only small pockets of strong
field able to rise into the upper layer. In simulations in which the magnetic
layer is generated by shear, we find that the shear velocity is not necessarily
required to exceed that of the pumping (therefore the kinetic energy of the
shear is not required to exceed that of the overlying convection), for strong
localised pockets of magnetic field to be produced which can rise into the
upper layer. This is because magnetic flux pumping acts to store the field
below the interface, allowing it to be amplified both by the shear, and by
vortical fluid motions, until pockets of field can achieve sufficient strength
to rise into the upper layer. In addition, we find that the interface between
the two layers is a natural location for the production of strong vertical
gradients in the magnetic field. If these gradients are sufficiently strong to
allow the development of magnetic buoyancy instabilities, strong shear is not
necessarily required to drive them (c.f. previous work by Vasil & Brummell). We
find that the addition of magnetic flux pumping appears to be able to assist
shear-driven magnetic buoyancy in producing strong flux concentrations that can
rise into the convection zone from the radiative interior.
