Abstract <p>The purpose of the study has been to build a self-consistent gas-dynamic model of the accretion disk of a compact astrophysical object with allowance for 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 one. Physical proton viscosity is not sufficient 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 with allowance for the generally accepted turbulent viscosity, we want to demonstrate a solution with such instability. In a recently published study on Kepler disk braking, we have been 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. While the development of small-scale shear instability on the surface of a neutron star for a Kepler disk has not been demonstrated in calculations. In this study, we have examined 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.</p>