Non-axisymmetric hydrodynamical instability and transition
to turbulence in accretion discs
Gaseous disks are stable to all LOCAL non-axisymmetric disturbances
(Goldreich and Lynden-Bell 1965),
but can be unstable GLOBALLY to non-axisymmetric modes (m>0).
The density waves are just sound waves (the non-axisymmetric instability in this
case is reffered to as the Papaloizou-Pringle -PP instability; Papaloizou-Pringle
1984). The inner radial boundary is reflective and the instability is a corotation
reasonance (a reasonant cavity is formed between the corotation radius and
the inner boundary) and the modes grow due to the over-reflection of waves
at the corotation radius (the unstable modes are 'egde' modes, they grow
at the inner boundary). When the self gravity of the disk is important,
the waves are not sound waves but density waves (like in galaxies), and
the growth rate of the unstable modes is much larger (of the order of
the dynamical frequency). Click
here to see some simulations of non-axisymmetric
instability in self-gravitating disks.
A Papaloizou-Pringle instability develops in the inner region of a tidally
perturbed disk
(m=8 mode), (MPEG version 1.2Mb).
rotating counter clockwise
(stroboscopic effects might let you think the opposite). Only the
inner region of the disk is shown.
Numerical simulations of a tidal wave induced by a planet in a
protostellar disc, and the development of a Paploizou-Pringle instability
(initially an m=3 mode and eventually an m=2 mode) at the inner reflective boundary.
Click there to see (MPEG version 5Mb!).
A high order mode (m=19) of a
non-linear global instability (the Papaloizou-Pringle instability)
develops in the inner region of thin Keplerian disc, when
the viscosity is low and the inner boundary is reflective.
A black and white movie of the m=19 mode.
Eventually the disc becomes unstable and transits to turbulence.
The turbulence is confined to the innermost part of the disc.
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