Effect of low-frequency modulation on the acoustic radiation force in newtonian fluids

This study investigates the nature of the acoustic radiation force (ARF) in Newtonian fluids generated by a high-intensity sound field in situations when the latter is modulated using frequencies that are, relative to the frequency of sound, on the order of the Mach number. In the context of nonlinear acoustics, problems of this class turn out to be unresponsive to the usual asymptotic reduction via the concept of the ARF owing to the fact that the mean acoustic fields, computed as averages over the period of sound vibrations, retain rapid oscillation features of the latter. To meet the challenge, an asymptotic treatment is pursued within the framework of plane waves via a scaling paradigm that splits the temporal variable into "fast" and "slow" time, permitting one to track the contribution of (time-harmonic) sound and its modulation separately in the solution. In this setting the second-order asymptotic solution, written in terms of the "fast" time averages of acoustic fields, is shown to (i) be free of rapid oscillations, and (ii) permit compact formulation in terms of an initial-boundary value problem featuring the ARF that, for the first time, rationally captures the effect of sound modulation. The proposed framework of analysis is illustrated by the analytical solution for a sinusoidal modulation envelope with quiescent past, which both exposes the limitations of earlier treatments and highlights the generation of an ARF in a lossless fluid when a modulated, high-intensity sound field is propagated through it. On developing a finite difference solution to the original nonlinear problem, it is further shown that the featured "fast" time average can be approximated by a double "ordinary" time average (reckoned per period of sound vibrations) of the simulated nonlinear response.