טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAssaf Sternberg
SubjectA Search for Hydrodynamical Instabilities in Accretion Disks
DepartmentDepartment of Physics
Supervisor Professor Emeritus Regev Oded


Abstract

   Many astrophysical systems are thought to contain an accretion disk. The accretion process is possible only if angular momentum can be transferred outward while matter spirals inward, yet molecular viscosity, being too small, may not account as the cause of this transport. In the early 1970's it was suggested that turbulence may be the source of this transport, but no turbulence was shown to occur in the flow. In the early 1990's it was demonstrated that a weak magnetic field gives rise to the magneto-rotational instability (MRI), enabling the flow to become turbulent, thus providing the turbulence needed. For almost a decade the MRI was accepted to be the sole source of turbulence in accretion disks and the existence of a purely hydrodynamical driven turbulence has been questioned.

   Recently, some astrophysicists have started to question this paradigm. It is a well known fact that some shear flows tend to undergo transition to turbulence even for conditions that linear stability analysis claims should be stable. Therefore, it is plausible that even though linear stability analysis of a Keplerian disk gives no instability for all Reynolds numbers, it may still become unstable via some undetermined mechanism. Several recent works done in this field have shown the existence of transient growth in the kinetic energy for certain 2D perturbations of the disk flow, most of them using the small shearing box approximation. 

   In this work we focus on 3D perturbations of the flow within the small shearing box approximation. Using a fourth order correct Runga-Kutta scheme we perform a thorough study of initial conditions in order to map which conditions lead to a large amplification in the energy and the enstrophy. We have confirmed that transient growth can occur both in the energy and the enstrophy for leading modes, i.e. ones that propagate against the shear.