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Linear waves in a radiating and scattering grey medium

Authors:	Noboru Kaneko Shuichi Tamazawa Yôrô Ôno

Institution:	(1) Department of Physics, Faculty of Science, Hokkaido University, Sapporo, Japan

Abstract:	The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed $a_A^2 = {{\gamma P_g } \mathord{\left/ {\vphantom {{\gamma P_g } {\varrho + }}} \right. \kern-\nulldelimiterspace} {\varrho + }}{{\tfrac{4}{3}P_r } \mathord{\left/ {\vphantom {{\tfrac{4}{3}P_r } \varrho }} \right. \kern-\nulldelimiterspace} \varrho }$ is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When _eff1, the sound speeda _g ² =P _g/ and the propagating speed of radiative disturbancea _f ² =fc ² appear as the modified classical and radiation-induced modes respectively, wheref is the Eddington factor. When _eff1, the isentropic sound speeda _s ² =(P _g+P _r/ appears in the equilibrium case, and the radiation acoustic speeda _A ² appears in the scattering case. The dispersion relation of the harmonic solution is numerically calculated. The result shows that the wave pattern depends critically on the ratio=P _g/(P _g+P _r). When $\beta \gtrsim \frac{1}{2}$ , the speeda _S anda _A arise from the modified classical mode, and when $\beta \lesssim \frac{1}{2}$ , they originate from the radiation-induced mode.

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