Interaction of two-dimensional spots with a heat releasing/absorbing shock wave: linear interaction approximation results

Abstract

The canonical interaction between a two-dimensional weak Gaussian disturbance (entropy spot, density spot, weak vortex) with an exothermic/endothermic planar shock wave is studied via the linear interaction approximation. To this end, a unified framework based on an extended Kovásznay decomposition that simultaneously accounts for non-acoustic density disturbances along with a poloidal–toroidal splitting of the vorticity mode and for heat release is proposed. An extended version of Chu’s definition for the energy of disturbances in compressible flows encompassing multi-component mixtures of gases is also proposed. This new definition precludes spurious non-normal phenomena when computing the total energy of extended Kovásznay modes. Detailed results are provided for three cases, along with fully general expressions for mixed solutions that combine incoming vortical, entropy and density disturbances.