Spontaneous emission in the linear problem of shock wave disturbance in a non-classical case

Abstract

The isentropic solutions of the linear problem of the shock wave disturbance are considered for a special (non-classical) case, where the both pre-shock and post-shock flows are subsonic. As it is known, only neutral stability is possible here, hence the spontaneous emission appears. The spontaneously emitted waves are studied and their general form is determined both for damped and oscillating initial values. For oscillating initial values both non-resonant and resonant cases are considered. Some interesting distinctions from the classical case are found. First, the spontaneously emitted acoustic waves are evanescent with respect to the variable normal to the shock but oscillate with respect to time. Second, only initial pre-shock vorticity wave may cause the resonance, while the resonance is impossible for initial acoustic both pre-shock and post-shock waves.