Abstract
Observations show that there are disks around certain stars that slowly rain down on the central (compact) object: accretion disks. The rate of depletion of the disk might be slow but is still larger than was expected on theoretical grounds. That is why it
has been suggested that
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the disks are turbulent. Because the disk is thin and rotating this turbulence might be related to
two-dimensional (2D) turbulence which is characterized by energy transfers towards small wave numbers and the formation of
2D-vortices. This hypothesis is investigated in this thesis by numerical simulations.
After an introduction, the numerical algorithm that was inplemented is discussed together with its relation to an accretion disk.
It performs well under the absence of discontinuities. The code is used to study 2D-turbulence under the influence of
background rotation with compressibility and a shearing background flow. The first is found to be of little consequence but the
shear flow alters 2D-turbulence siginificantly. Only prograde vortices of enough strength are able to withstand the shear flow.
The size of the vortices in the cross stream direction is also found to be smaller than the equivalent of the thickness of an
accretion disk. These circulstances imply that the assumption of two-dimensionality is questionable so that 2D-vortices might
not abound in accretion disks. However, the existence of such vortices is not ruled out and one such a cortex is studied in detail
in chapter 4. The internal structure of the vortex is well described by a balance between Coriolis, centrifugal and pressure
forces. The vortex is also accompanied by two spiral compressible waves. These are not responsible for the azimuthal drift of
the vortex, which results from secondary vortices, but they might be related to the small radial drift that is observed. Radial drift
leads to accretion but it is not very efficient. Multiple vortex interactions are the topic of tha last chapter and though interesting
the increase in accretion grows only linearly with the number of vortices.
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