Resonant Amplification of Turbulence by the Blast Wawes

Abstract

We discuss an idea whether spherical blast waves can amplify by a non-local resonant hydrodynamic mechanism inhomogeneities formed by turbulence or phase segregation in the interstellar medium. We consider the problem of a blast-wave-turbulence interaction in the Linear Interaction Approximation. Mathematically, this is an eigenvalue problem for finding the structure and amplitude of eigenfunctions describing the response of the shock-wave flow to forced oscillations by external perturbations in the ambient interstellar medium. Linear analysis shows that the blast wave can amplify density and vorticity perturbations for a wide range of length scales with amplification coefficients of up to 20, with amplification the greater, the larger the length. There also exist resonant harmonics for which the gain becomes formally infinite in the linear approximation. Their orbital wavenumbers are within the range of macro- ($l \sim 1$), meso- ($l \sim 20$) and microscopic ($l > 200$) scales. Since the resonance width is narrow: typically, $\Delta l <1$, resonance should select and amplify discrete isolated harmonics. We speculate as to a possible explanation of an observed regular filamentary structure of regular-shaped round supernova remnants such as SNR 1572, 1006 or 0509-67.5. Resonant mesoscales found ($l \approx 18 $) are surprisingly close to the observed scales ($l \approx 15$) of ripples in the shell's surface of SNR 0509-67.5.