Asymptotic laws of damping of weak continuous and shock waves in dust-laden gas

Abstract

Analytic investigations into the damping of perturbations in dust-laden gas have been restricted to self-similar flows [1, 2] and flows with a symmetry plane, it being assumed in the latter case that thermal and velocity equilibrium of the phases is established instantaneously [3–6], i.e., the relaxation time of the medium is short. In the present paper, asymptotic laws of damping are obtained for plane, cylindrical, and spherical shock and continuous waves whose amplitude and width are such that the acceleration of the particles and the change in their temperature can be ignored. It is assumed that between the phases there is heat transfer proportional to the temperature difference and frictional momentum transfer proportional to the difference between the velocities of the phases. The obtained laws of damping of plane waves are found to be entirely analogous to the laws of damping of magnetohydrodynamic waves in a medium with finite conductivity, when the presence of Joule dissipation and the additional ponderomotive force in the traveling wave or in the gas flow behind the shock wave leads to exponential damping of the wave amplitude [7–9].