  Recent analyses of the helioseismic data have produced evidence for a variety
of interesting dynamical behaviour associated with torsional oscillations. What
is not so far clear is whether these oscillations extend all the way to the
bottom of the convection zone and, if so, whether the oscillatory behaviour at
the top and the bottom of the convection zone is different. Attempts have been
made to understand such modes of behaviour within the framework of nonlinear
dynamo models which include the nonlinear action of the Lorentz force of the
dynamo generated magnetic field on the solar angular velocity. One aspect of
these models that remains uncertain is the nature of the boundary conditions on
the magnetic field. Here by employing a range of physically plausible boundary
conditions, we show that for near-critical and moderately supercritical dynamo
regimes, the oscillations extend all the way down to the bottom of the
convection zone. Thus, such penetration is an extremely robust feature of the
models considered. We also find parameter ranges for which the supercritical
models show spatiotemporal fragmentation for a range of choices of boundary
conditions. Given their observational importance, we also make a comparative
study of the amplitude of torsional oscillations as a function of the boundary
conditions.
