8 research outputs found
Linear and Weakly Nonlinear Analysis of the Magneto-Rotational-Instability in Thin Keplerian Discs
The linear instability of thin, vertically-isothermal Keplerian discs, under
the influence of axial magnetic field is investigated. Solutions of the
stability problem are found explicitly by asymptotic expansions in the small
aspect ratio of the disc. It is shown that the perturbations are decoupled into
in-plane and vertical modes. Exact expressions for the growth rates as well as
the number of unstable modes are derived. Those are the discrete counterpart of
the continuous infinite homogeneous cylinder magnetorotational (MRI) spectrum.
In addition, a weakly nonlinear analysis of the MRI is performed. It is shown
that near the instability threshold the latter is saturated by the stable
magnetoacoustic modes.Comment: 18 pages, 6 figures, to appear in the proceedings of the workshop
"Waves and Instabilities in Space and Astrophysical plasmas" (WISAP-2011),
June 201
Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs
The short time evolution of three dimensional small perturbations is studied.
Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to
host intensive hydrodynamical activity in the shape of non modal growth of
initial small perturbations. Two mechanisms that lead to such behavior are
identified and studied, namely, non-resonant excitation of vertically confined
sound waves by stable planar inertia-coriolis modes that results in linear
growth with time, as well as resonant coupling of those two modes that leads to
a quadratic growth of the initial perturbations. It is further speculated that
the non modal growth can give rise to secondary strato-rotational instabilities
and thus lead to a new route to turbulence generation in thin discs
An optimal transient growth of small perturbations in thin gaseous discs
A thin gaseous disc with an almost keplerian angular velocity profile,
bounded by a free surface and rotating around point-mass gravitating object is
nearly spectrally stable. Despite that the substantial transient growth of
linear perturbations measured by the evolution of their acoustic energy is
possible. This fact is demonstrated for the simple model of a non-viscous
polytropic thin disc of a finite radial size where the small adiabatic
perturbations are considered as a linear combination of neutral modes with a
corotational radius located beyond the outer boundary of the flow.Comment: 15 pages, 5 figures, accepted for publication in Ast