Numerical simulations of instability in the shell of a supernova remnant expanding in a weakly inhomogeneous interstellar medium

Astronomical observations show that the supernova remnants, even with a close to spherical shape, usually have multiscale ripple-like distortions. For example 15 bends on the shock front are clearly visible in the remnant 0509-67.5. The global instability of the flow is considered as one of the possible mechanisms for generating such structures. In the frame of linear analysis [26] was shown that this instability has a resonance character. It means that the perturbations with a certain wavelength number should grow faster, therefore ripples in the remnant shell will manifest itself predominantly in a certain range of scales. In this paper we present the results of numerical simulations of the nonlinear stage of this instability, caused by small perturbations in the external environment, depending on their scale and intensity. The unpertubed gas is supposed to has a power-law spartial dependence $\rho_0(r) \sim r^{-\omega}$, where $\omega$ is a constant. The blast wave generated by a supernova expolosion is descibed by a Sedov type similarity solution. We have developed two-dimensional numerical model of adiabatic flow with a blast wave in a comoving frame of reference based on parallel code AstroChemHydro [1]. It was shown that, according to the predictions of linear analysis, perturbations in the external flow amplify behind the front of the shock wave, which leads to the development of convective instability and the development of turbulence. The results of numerical simulations demonstrated that in shell-type flows (for $ \omega = 2 {,} 7 $ and $ \gamma = 4/3 $) external disturbances along with the characteristic rearrangement of the shock front and turbulization of the flow behind it, cause the formation of radially elongated filaments with a vortex structure behind the shock, the number of which is determined by the harmonic number of the perturbation $ l $.