Gas-dynamic instabilities in a two-dimensional boundary layer during accretion

The purpose of the work is to build a self-consistent gas-dynamic model of the accretion disk of a compact astrophysical object, taking into account viscosity. The matter falling on a compact object consists of proton gas, electrons, and radiation arising from the braking of a rotating gas at a speed comparable to light. Physical proton viscosity is not enough in the gas-dynamic accretion model with laminar flow. It is necessary to introduce the so-called turbulent viscosity, probably arising from the development of instabilities, to explain the loss of the disk angular momentum. With a quantitative mathematical model of gas dynamics, taking into account the generally accepted turbulent viscosity, we want to demonstrate a solution with such instability. In a recently published work on Kepler disk braking, we were able to obtain only large-scale vortex structures arising from azimuthal perturbations, for example, due to tidal effects, and demonstrated an increase in disk braking against a neutron star due to these vortex structures. And the development of small-scale shear instability on the surface of a neutron star for a Kepler disk was not demonstrated in calculations. In this work, we examine a non-Keplerian disk with a non-zero negative radial velocity, ensuring the flow of matter to the surface of a compact star, as a result of which shear instability and turbulence appear.

neutron star, accretion disk, gamma ray burst, conservative finite difference scheme