Density-Evolution:
(in r-phi) for standard model:
gif-file.
Times are in units of the orbital period at r=1.
Initially an axially symmetric disturbance appears, which turns
into a trailing spiral arm.
There is no tendency in my runs to produce a leading spiral.
Growth-Rates:
Growth of m=1 to m=5 Modes for basic model.
png-file.
Time in units of orbital period at R=1.
Numerical Study: Growth of m=1 Fouriermodes for the basic model (6) using different numerics (inertial-rotating frame, explicit-implicit viscosity, no-dimensional splitting) png-file. The numerical issues play no visible role.
Resolution Study:
Growth of m=1 Fouriermode for the
standard model at different resolutions.
png-file.
Remarks: There should be some influence of the resolution on the
growth-rates, as the wavenumber k appears in the dispersion
relation.
To clearify things I plotted some results for a given radial resolution
of 128 Gridpoints (png-file)
but varying phi-points.
From the plot is seems that the growthrates are pretty much
independent of the phi-resolution, once numerical convergence
has been reached.
From the first plot there seems to be the tendency that for increasing
resolution in the radial direction (higher k ??) the growthrates
become smaller!
Viscosity:
Variation of the kinematic Viscosity. Factor 2 lower (9d, 9g)
and higher (9f, 9h). The two models (9g, 9h) differ from the others
only in the initial setup (different random routine) and are
performed in the inertial frame.
png-file.
Evolution of Sigma(r):
mpeg-movie
-- Time in units of t_visc!
Older Run: In the Rotating Frame (!!)
mpeg-movie
-- Caused by the rotating frame the spirals move fast, apparently reversed.