Recent observations of several protoplanetary discs have found
evidence of departures from flat, circular motion in the inner
regions of the disc. One possible explanation for these observations
is a disc warp, which could be induced by a planet on a misaligned orbit.
We present three-dimensional numerical simulations of the tidal
interaction between a protoplanetary disc and a misaligned planet.
For low planet masses we show that our simulations accurately model
the evolution of inclined planet orbit (up to moderate inclinations).
For a planet massive enough to carve a gap, the disc is separated into
two components and the gas interior and exterior to the planet orbit evolve
separately, forming an inner and outer disc. Due to the inclination of the
planet, a warp develops across the planet orbit such that there is a relative
tilt and twist between these discs. We show that when other parameters are
held constant, the relative inclination that develops between the inner
and outer disc depends on the outer radius of the total disc modelled.
For a given disc mass, our results suggest that the observational relevance
of the warp depends more strongly on the mass of the planet rather than
the inclination of the orbit.
We demonstrate that the compact, thick disc formed in a tidal
disruption event may be unstable to non-axisymmetric perturbations
in the form of the Papaloizou-Pringle instability. We show this
can lead to rapid redistribution of angular momentum that can be
parametrized in terms of an effective Shakura-Sunyaev α parameter.
For remnants that have initially very weak magnetic fields, this may be
responsible for driving mass accretion prior to the onset of the
magnetorotational instability. We thus identify a method by which
the torus formed in tidal disruption event may be significantly
accreted before the magnetorotational instability is established.
We demonstrate the importance of general relativistic apsidal
precession in warped black hole accretion discs by comparing three-dimensional
smoothed particle hydrodynamic simulations in which this effect is first
neglected, and then included. If apsidal precession is neglected, we confirm
the results of an earlier magnetohydrodynamic simulation which made this
assumption, showing that at least in this case the α viscosity model produces
very similar results to those of simulations where angular momentum transport
is due to the magnetorotational instability. Including apsidal precession
significantly changes the predicted disc evolution. For moderately inclined
discs thick enough that tilt is transported by bending waves, we find a disc
tilt which is non-zero at the inner disc edge and oscillates with radius,
consistent with published analytic results. For larger inclinations, we find disc breaking.
We investigate the effect of black hole spin on warped or misaligned
accretion discs - in particular (i) whether or not the inner disc edge
aligns with the black hole spin and (ii) whether the disc can maintain
a smooth transition between an aligned inner disc and a misaligned outer
disc, known as the Bardeen-Petterson effect. We employ high-resolution
3D smoothed particle hydrodynamics simulations of α-discs subject to
Lense-Thirring precession, focusing on the bending wave regime where the
disc viscosity is smaller than the aspect ratio α ≲ H/R. We first address
the controversy in the literature regarding possible steady-state oscillations
of the tilt close to the black hole. We successfully recover such oscillations
in 3D at both small and moderate inclinations (≲15°), provided both
Lense-Thirring and Einstein precession are present, sufficient resolution
is employed, and provided the disc is not so thick so as to simply accrete
misaligned. Secondly, we find that discs inclined by more than a few
degrees in general steepen and break rather than maintain a smooth transition,
again in contrast to previous findings, but only once the disc scaleheight
is adequately resolved. Finally, we find that when the disc plane is misaligned
to the black hole spin by a large angle, the disc `tears' into discrete rings
which precess effectively independently and cause rapid accretion, consistent
with previous findings in the diffusive regime (α ≳ H/R). Thus, misalignment
between the disc and the spin axis of the black hole provides a robust mechanism
for growing black holes quickly, regardless of whether the disc is thick or thin.