Acoustic propagation in inhomogeneous fluids: regularization via the introduction of fine particles

Abstract

It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.