Non-linear waves in radiation-gas-dynamics

Abstract

This work is a sequel to a previous paper where a new set of equations tor one-dimensional motion in Radiation-Gas-Dynamics (RGD) has been derived. These equations are valid for an arbitrary but constant value of opacity and for all values of β, the ratio of the gas pressure to the total pressure, and they clearly show the existence of radiation induced waves, which have been called "precursor radiation" by Lick and Moore. In this paper non-linear waves, with special refeience to the formation of shock waves in stellar medium, are discussed by a general method developed by Whitham. §2 contains a general discussion of the equations of motion. The interactions of waves of different orders are discussed and damping distances, decay times and diffusion coefficients are determined . The terms giving rise to the fifth, fourth and third order waves are found out and it is shown that the equations with third order terms can be used as approximate equations in RGD, when one is interested in changes in flow and physical parameters over distances which are large compared to the mean free path of radiation, i.e. " flow in large". The formation of shock waves from a given compression wave is discussed by the method of characteristics and it has been found that a discontinuous front is formed only if the initial disturbance is sufficiently strong. Simple waves and Rankine-Hugoniot conditions for shock waves are also considered. It is found that the Rankine-Hugoniot conditions, derived by Sachs apply only to shock waves in " flow in large ". Formation of shock waves in spherical, cylindrical and plane motion is also considered and the results obtoined by Pack are rederived by a very simple alternative method.