טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGitelman Larissa
SubjectMeridional Flow and Vertical Structure of Accretion Disks
DepartmentDepartment of Applied Mathematics
Supervisor Professor Emeritus Oded Regev


Abstract

We present numerical solutions of the meridional flow in axisymmetric   thin viscous accretion disk models. The solutions are obtained by simplifying and approximating first the equations, using systematic asymptotic expansions in the  small parameter  e measuring the relative disk thickness.  The equation of state was assumed to be of an ideal gas and  the thermal problem was solved using the radiation diffusion     approximation.

Hence, the vertical structure is solved with thermal effects  explicitly included via an energy equation, containing viscous dissipation  and radiative losses (treated in the diffusion approximation). The inclusion of the energy equation  will force  us to use some quite straightforward numerical  ODE integrations.

Carrying out the expansion to second order in  e we obtain, for low enough values of the viscosity  parameter a solutions containing backflows.

  For all values  aastag   of the viscosity parameter,  we find  significant backflow in the midplane of the disk occuring at all radii  larger than a certain value; however, in the inner regions of the disk the fluid always flows toward the accreting object. The region of backflow  is separated from the region of inflow by a surface flaring outwards from  a circular locus of stagnation points situated in the midplane of the disk.

The value we find is   astag    @   0.7   and the reason for its being only an approximation is the fact that in a   numerical calculation like ours the truncation error renders the result unreliable for large    r ,  specifically for    rstag   @   10^{3} r+ .

These results are similar to theapproximate results previously  found by Urpin (1984)(which however contained  an inconsistency and were valid only for large radii) and the asymptotic  analytical  solutions of Kluzniak and Kita (1997) (valid only for polytropic disks). Several  two-dimensional time dependent numerical simulations of thin viscous disks have also reavealed flow patterns of this type.

The existence of backflows may have important  consequences on the properties of accretion disks in  astrophysical objects.