Instability of relativistic shock waves: Numerical study on the basis of model equation of state

Abstract

The behavior of unstable relativistic shock waves is studied with the use of specially developed model equation of state (EOS). The EOS admits the Taub-Hugoniot adiabats with segments on which the criteria of the relativistic shock wave stability are violated. The instability segments are overlapped by the regions with ambiguous representation of the shock-wave discontinuity. The simulations are fulfilled for L < − 1 and L > (1 + 2M + v0v1)/(1 − v0v1) instability conditions, where L is relativistic analog of Dyakov parameter, M is post-shock Mach number, v0 and v1 are pre- and post-shock velocities in the shock attached reference frame. Under the condition of ambiguous representation of the shock-wave discontinuity in the former case the splitting of the unstable shock with formation of a composite compression wave with Lorentz factor dependent structure is observed. It is shown that the latter condition leads to two-dimensional non-stationary solutions characterized by presence of strong transverse waves.