Detonation waves in relativistic hydrodynamics.

Abstract

This paper is concerned with an algebraic study of the equations of detonation waves in relativistic hydrodynamics taking into account the pressure and the energy of thermal radiation. A new approach to shock and detonation wavefronts is outlined. The fluid under consideration is assumed to be perfect (nonviscous and nonconducting) and to obey the following equation of state: p=(\ensuremath{\gamma}-1)\ensuremath{\rho} where p, \ensuremath{\rho}, and \ensuremath{\gamma} are the pressure, the total energy density, and the adiabatic index, respectively. The solutions of the equations of detonation waves are reduced to the problem of finding physically acceptable roots of a quadratic polynomial \ensuremath{\Pi}(X) where X is the ratio \ensuremath{\tau}/${\mathrm{\ensuremath{\tau}}}_{0}$ of dynamical volumes behind and ahead of the detonation wave. The existence and the locations of zeros of this polynomial allow it to be shown that if the equation of state of the burnt fluid is known then the variables characterizing the unburnt fluid obey well-defined physical relations.