  I present results from a set of 3D spherical-shell MHD simulations of the
buoyant rise of active region flux tubes in the solar interior which put new
constraints on the initial twist of the subsurface tubes in order for them to
emerge with tilt angles consistent with the observed Joy's law for the mean
tilt of solar active regions. Due to the asymmetric stretching of the
$\Omega$-shaped tube by the Coriolis force, a field strength asymmetry develops
with the leading side having a greater field strength and thus being more
cohesive compared to the following side. Furthermore, the magnetic flux in the
leading leg shows more coherent values of local twist $\alpha \equiv {\bf J}
\cdot {\bf B} / B^2$, whereas the values in the following leg show large
fluctuations and are of mixed signs.
