Propagation of rapid pulses through a two-phase mixture of gas and dust particles

Abstract

Small and finite amplitude pulses of an arbitrary initial profile propagating into a uniform region of a dusty gas have been studied. Solutions based on an asymptotic simple wave procedure are presented under the approximation that the characteristic length of the signal is much shorter than the characteristic length of the medium. The modulation of simple waves by the dissipative effects owing to the presence of solid particles, and the effect of nonlinearity leading to wave distortion and shock formation are discussed. In the small amplitude limit, a solution up to the second order is obtained, and numerical computations are carried out over one complete cycle for typical values of the physical parameters involved in the solution. The second order solution, in contrast to the first order, depends on the precursor wavelets and exhibits changes in those parameters which remained constant in the first order approximation. Finally, the second order solution is used to describe the far field behavior of weak shocks.